Auflistung Mathematics nach Titel
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Jovanović, Milan (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/58 Dateien zu dieser Ressource: 1
phdMilanJovanovic.pdf ( 1.497Mb ) -
Lazarević, Ivan (Beograd , 2022)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
Ivan_teza20042022.pdf ( 1.428Mb ) -
Jović, Aleksandar (Beograd , 2021)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
A.Jovic_doktorska_disertacija.pdf ( 1.280Mb ) -
Vicanović, Jelena (Beograd , 2024)[more][less]
Zusammenfassung: A convex continuous-time maximization problem is formulated and the nec- essary optimality conditions in the infinite-dimensional case are obtained. As a main tool for obtaining optimal conditions in this dissertation we use the new theorem of the alternative. Since there’s no a differentiability assumption, we perform a linearization of the problem using subdifferentials. It is proved that the multiplier with the objective function won’t be equal to zero. It was also shown that if the linear and non-linear constraints are separated, with additional assumptions it can be guaranteed that the multiplier with non-linear constraints will also be non-zero. In the following, an integral constraint is added to the original convex problem, so that a Lyapunov-type problem, i.e. an isoperimetric problem, is considered. Lin- earization of the problem using subdifferentials proved to be a practical way to ignore the lack of differentiability, so the optimality conditions were derived in a similar way. It is shown that the obtained results will also be valid for the vector case of the isoperimetric problem. Additionally, the optimality conditions for the smooth problem were considered. On the minimization problem, it was shown that the necessary conditions of Karush-Kuhn-Tucker type will be valid with the additional regularity constraint condition. Also, any point that satisfies the mentioned optimality conditions will be a global minimum. URI: http://hdl.handle.net/123456789/5676 Dateien zu dieser Ressource: 1
J.Vicanovic_doktorska_disertacija.pdf ( 2.198Mb ) -
Jovanović Spasojević, Tanja (Beograd , 2022)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
Jovanovic_Spasojevic_Tanja.pdf ( 1.643Mb ) -
Šćepanović, Radoje (Belgrade , 1978)[more][less]
URI: http://hdl.handle.net/123456789/204 Dateien zu dieser Ressource: 1
phdRadojeScepanovic.pdf ( 1.786Mb ) -
Rašajski, Marija (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/177 Dateien zu dieser Ressource: 1
Phd-Marija.Rasajski.pdf ( 3.705Mb ) -
Trifunović, Milomir (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/343 Dateien zu dieser Ressource: 1
phdMilomirTrifunovic.pdf ( 2.571Mb ) -
Mišić, Miodrag (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/64 Dateien zu dieser Ressource: 1
phdMiodragMisic.pdf ( 2.242Mb ) -
Kastrati, Ruzhdi (Priština , 1989)[more][less]
URI: http://hdl.handle.net/123456789/4129 Dateien zu dieser Ressource: 1
Fourie_te_disa_klasa.PDF ( 1.942Mb ) -
Lučić, Blagota (Belgrade , 1985)[more][less]
URI: http://hdl.handle.net/123456789/52 Dateien zu dieser Ressource: 1
phdBlagotaLucic.pdf ( 1.076Mb )
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