Browsing Doctoral Dissertations by Title
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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 ) -
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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Jelović, Ana (Beograd , 2022)[more][less]
Abstract: n the first part of this dissertation different repeat types are defined as well as repeats that satisfy motif masks. A method for precise repeat finding in input sequences of arbitrary length has been described. As the input sequences can be very long, the number of found repeats can also be large. For that reason it is important that the method also includes filtering found repeats based on the expected number of their occurrences. The method was first applied to protein sequences in which experimentally confirmed T-cell epitopes from the IEDB database were registered. Association rules were applied to the found repeats in order to construct a model that would enable the prediction of the positions of T-cell epitopes in protein sequences. In this way, it would indicate to researchers a region in the protein sequence where an epitope can be expected with high confidence. In the case of T-cell epitopes, a large number of rules with high confidence was found. These rules can be considered as reliable predictors of the position of T-cell epitopes within the protein sequences. Based on the results found, association rules were formed that characterize the epitopes and the repeats associated with them in more detail. As a large number of results were found, only their part is presented in this disser- tation. On the basis of the strings that determine the repeat, a motif mask that the repeat needs to satisfy was searched for. The entire procedure was applied to both direct non-complementary repeats and indirect non-complementary repeats. With similar results, the entire procedure was applied to B-cell epitopes on data from the IEDB database. Data on experimentally confirmed short linear motifs were taken from the ELM database. In protein sequences where short linear motifs were registered, repeats were searched for and association rules were applied to them. The rules with high confidence have been singled out in particular. On the basis of the results found, motif masks that repeats with high confidence would satisfy were searched for. URI: http://hdl.handle.net/123456789/5442 Files in this item: 1
Ana_Jelovic_tekst_doktorata.pdf ( 6.127Mb )
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