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Now showing items 407-426 of 426
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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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Popović, Nikola (Belgrade)[more][less]
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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 ) -
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 ) -
Jovanović Spasojević, Tanja (Beograd , 2022)[more][less]
Abstract: In this thesis, subjects of consideration are the embeddings theorems of weighted Bergman spaces in Lp-spaces, as well as embeddings theorems of harmonic mixed norm spaces. The first part of the thesis generalizes the theorems of embeddings Bergman spaces into Lp(μ)-spaces, where μ is a Borel measure on a given domain. They have been earlier studied on domains such as unit ball and upper half-space. Generalization refers to bounded domains Ω ⊂ Rn with C1 boundary. This embedding will be valid to any p > 0, whenever the measure of the spaces Lp satisfies the Carledon condition. Reverse the direction will be valid only in case if p > 1 + α+2 n−2 . The second part of the dissertation also generalizes the embeddings theorems of mixed norm spaces of harmonic functions on a unit ball, where the generalization is applied to the domain Ω ⊂ Rn with C1 boundary. However, in addition we are obtaining another important result relating to the limitation of the maximum operators in the mixed norm on the general domain for the class of QNS functions. URI: http://hdl.handle.net/123456789/5378 Files in this item: 1
Jovanovic_Spasojevic_Tanja.pdf ( 1.643Mb ) -
Šćepanović, Radoje (Belgrade , 1978)[more][less]
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Rašajski, Marija (Belgrade)[more][less]
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Trifunović, Milomir (Belgrade)[more][less]
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Mišić, Miodrag (Belgrade)[more][less]
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Kastrati, Ruzhdi (Priština , 1989)[more][less]
URI: http://hdl.handle.net/123456789/4129 Files in this item: 1
Fourie_te_disa_klasa.PDF ( 1.942Mb ) -
Lučić, Blagota (Belgrade , 1985)[more][less]
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Now showing items 407-426 of 426