Browsing Doctoral Dissertations by Title
Strana 1-20 od 598
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Petković, Đorđe (Vienna , 1893)[more][less]
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Rajović, Miloje (Belgrade , 1985)[more][less]
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Duborija, Stojan (Belgrade , 1981)[more][less]
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Dubarija, Stojan (Beograd , 1981)[more][less]
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Lukačević, Ilija (Belgrade , 1968)[more][less]
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Nikolić, Jovana (Beograd , 2017)[more][less]
Abstract: In this doctoral dissertation we de ne and investigate spectral invariants in Floer homology for conormal bundle and Floer homology of an open sub- set. As a key step to well de ned spectral invariants we give a construction of Piunikhin-Salamon-Schwarz isomorphism in both of these homologies. Ad- ditional algebraic structures, such as a product on Floer homology, give us various inequalities between spectral invariants. We can compare spectral in- variants from di erent Floer homologies by observing appropriate perturbed holomorphic Riemmanian surfaces with boundary. URI: http://hdl.handle.net/123456789/4506 Files in this item: 1
J_Nikolic_doktteza.pdf ( 2.076Mb ) -
Božović, Vladimir (Boca Raton, Florida , 2008)[more][less]
Abstract: The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed. URI: http://hdl.handle.net/123456789/296 Files in this item: 1
phdVladimirBozovic.pdf ( 1.070Mb ) -
Lončar, Jovan (Sarajevo)[more][less]
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Jovanović, Božidar (Belgrade , 1973)[more][less]
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Radojčić, Miloš (Belgrade)[more][less]
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Ralević, Nebojša (Belgrade)[more][less]
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Damjanović, Boško (Belgrade)[more][less]
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Milošević, Nela (Beograd , 2015)[more][less]
Abstract: This dissertation examines simplicial complexes associated with commutative rings with unity. In general, a combinatorial object can be attached to a ring in many di erent ways, and in this dissertation we examine several simplicial complexes attached to rings which give interesting results. Focus of this thesis is determining the homotopy type of geometric realization of these simplicial complexes, when it is possible. For a partially ordered set of nontrivial ideals in a commutative ring with identity, we investigate order complex and determine its homotopy type for the general case. Simplicial complex can also be associated to a ring indirectly, as an independence complex of some graph or hypergraph which is associated to that ring. For the comaximal graph of commutative ring with identity we de ne its independence complex and determine its homotopy type for general commutative rings with identity. This thesis also focuses on the study of zero-divisors, by investigating ideals which are zero-divisors and de ning zero-divisor ideal complex. The homotopy type of geometric realization of this simplicial complex is determined for rings that are nite and for rings that have in nitely many maximal ideals. In this part of the thesis, we use the discrete Morse theory for simplicial complexes. The theorems proven in this dissertation are then applied to certain classes of commutative rings, which gives us some interesting combinatorial results. URI: http://hdl.handle.net/123456789/4421 Files in this item: 1
Nela_Milosevic_Teza.pdf ( 20.62Mb ) -
Cvetković, Milica (Niš , 2013)[more][less]
Abstract: This work provides the surface shape analysis in R3 using the shape operator, i.e. using the curvatures as well as curvature's functionals such as the Willmore energy. Then, there were considered changes of surfaces' geometric characteristics under infinitesimal deformations, and specialy, curvature based functionals variations under infinitesimal bending of surface. Special kinds of ruled surfaces were analysed from geometrical and constructional point of view, and pointed to their wide use. At last, there is a generalization by considering the Finsler and the generalized Finsler spaces. URI: http://hdl.handle.net/123456789/3813 Files in this item: 1
2014_01_22_cm.pdf ( 1.476Mb ) -
Ilić, Dejan (Beograd , 2016)[more][less]
Abstract: We study linearly ordered structures and their complete theories. The main technical tools used in the analysis are condensations, i.e. partitioning the ordering into convex parts and then studying the quotient structure and that of the parts. We introduce a uniformly definable condensation relation cδ that decomposes the ordering into largest convex pieces whose first order theory is simple: they are either dense or discrete orderings. We study cδ quotient structures that are expansions of certain simple countable discrete orderings and give a precise description of those having Cantor Bendixson rank 1. We also use the condensation cδ to prove that any linear ordering expanded by finitely many unary predicates and equivalence relations with convex classes is interpretable in a pure linear ordering. We introduce notions of linear and strong linear binarity for linearly ordered structures and their complete theories. In the case of a theory, the defining condition expresses a property of the automorphism group of its saturated model. We prove that any complete theory of a linear ordering with unary predicates and equivalence relations with convex classes is strongly linearly binary. The main result states that a strongly linearly binary structure is definitionally equivalent to a linear ordering with unary predicates and equivalence relation with convex classes added. In the proof we give a description of definable sets in any linear ordering with unary predicates and equivalence relations with convex classes. URI: http://hdl.handle.net/123456789/4452 Files in this item: 1
disertacija_IlicDejan.pdf ( 756.7Kb ) -
Čvorović - Hajdinjak, Iva (Beograd , 2025)[more][less]
Abstract: This doctoral dissertation addresses the development and application of advanced methods for analyzing the temporal variability of active galactic nuclei (AGN) through the modeling of their optical light curves. The research integrates unsupervised and generative learning techniques, by combining Self- Organizing Maps (SOM) for data preprocessing and Conditional Neural Processes (CNP) for light curve prediction. For the first time in the study of AGN light curves, clustering via SOM has been implemented for preprocessing, alongside the application of CNP for modeling variability. This innovative approach facilitates a more effective modeling of light curves characterized by uneven sampling and missing observations. The QNPy software package was developed and optimized for large-scale parallel processing of extensive time series data. The proposed methodology was validated using light curves from the All-Sky Automated Survey for SuperNovae (ASAS-SN) and the SWIFT/BAT mission, covering a broad range of time scales and variability. The analysis prove that clustering light curves with SOM enhances the performance of neural process, particularly for objects exhibiting simpler variability patterns. The effects of SOM hyperparameters on clustering and prediction performance were carefully examined. The models were validated using loss function and mean squared error evaluations on real data. The proposed methodology shows strong potential for scalable processing of the large time-series data, anticipated in upcoming projects such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time, enabling automated classification, anomaly detection, and the extraction of scientifically significant objects from catalogs containing hundreds of millions of sources. URI: http://hdl.handle.net/123456789/5766 Files in this item: 1
doktorska_disertacija_iva_cvorovic_hajdinjak.pdf ( 7.248Mb ) -
Pucanović, S. Zoran (Belgrade , 2012)[more][less]
Abstract: This dissertation examines various properties of commutative rings and modules using algebraic combinatorial methods. If the graph is properly associated to a ring R or to an R-module M, then examination of its properties gives useful information about the ring R or R-module M. This thesis discusses the determination of the radius of the total graph of a commutative ring R in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the R-module M and relations between the total graph of the ring R and its extensions are also dealt with. The total graph of a module, a generalization of the total graph of a ring is presented. Various properties are proved and some relations to the total graph of a ring as well as to the zero-divisor graph are established. To gain a better understanding of clean rings and their relatives, the clean graph C¡(R) of a commutative ring with identity is introduced and its various proper- ties established. Further investigation of clean graphs leads to additional results concerning other classes of commutative rings. One of the topics of this thesis is the investigation of the properties of the cor- responding line graph L(T¡(R)) of the total graph T¡(R). The classi¯cation of all commutative rings whose line graphs of the total graph are planar or toroidal is given. It is shown that for every integer g ¸ 0 there are only ¯nitely many commutative rings such that °(L(T¡(R))) = g. Also, in this thesis all toroidal graphs which are intersection graphs of ideals of a commutative ring R are classi¯ed. An improvement over the previous results concerning the planarity of these graphs is presented. URI: http://hdl.handle.net/123456789/2489 Files in this item: 1
Pucanovic_Zoran.pdf ( 2.059Mb ) -
Brkić, Zaharije (Belgrade , 1958)[more][less]
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Radunović, Desanka (Belgrade , 1984)[more][less]
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Dačić, Miodrag (, 1998)[more][less]
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