Browsing Mathematics by Title

Mostafa, Attila (Beograd , 2015)[more][less]
Abstract: First of all I would like to express my praises and sincere thanks to almighty Allah, start with no end and end will never start, for his divine assistance and guidance, which gave me the ability to succeed. I Thank you Allah, for life, health, and the energy that you have given me to reach my professional goals. Iwould like to gratefully and sincerely thank my supervisor Prof PhD Miodrag Mateljevi´c as well as dr Miljan Kneževi´c for their guidance, understanding, patience, and most importantly, their friendship during my graduate studies at my faculty. Their mentorship was paramount in providing a wellrounded experience consistent my career goals. My sincere appreciation, thanks and gratitude to all the academic staff members of Faculty of Mathematics, University of Belgrade. I would to thank Libyan Embassy in Belgrade to provide material and moral support. URI: http://hdl.handle.net/123456789/4339 Files in this item: 1
Attia Mostafa_thesis.pdf ( 3.337Mb ) 
Louka, Hana Almoner (Beograd , 2016)[more][less]
Abstract: This thesis has been written under the supervision of my mentor dr. Vladimir Bo zin at the University of Belgrade in the academic year 2016. The topic of this thesis is quantum information theory, with special attention to quantum contract signing protocols. The thesis is divided into four chapters. Chapter 1 gives introduction to Quantum mechanics and necessary mathematical background. Chapter 2 is about quantum information theory. Quantum algorithms, including Schor's and Grover's, are described. Chapter 3 deals with classical contract signing, and cryptography. Also discussed is the RSA algorithm and BB84 quantum key distribution. Chapter 4 describes quantum signing protocol, and proves, among other things, asymptotic behavior for probability of cheating. URI: http://hdl.handle.net/123456789/4342 Files in this item: 1
hanathesis21.pdf ( 711.2Kb ) 
Davidović, Tatjana (Belgrade , 2006)[more][less]

Banković, Dragić (Belgrade , 1980)[more][less]

Savić, Branko (Belgrade)[more][less]

Pantić, Dražen (Belgrade)[more][less]

Lepović, Mirko (Beograd , 1991)[more][less]
URI: http://hdl.handle.net/123456789/4138 Files in this item: 1
Spektralna_teorija_grafova.PDF ( 4.283Mb ) 
Marić, Miroslav (Belgrade)[more][less]

Lazić, Mirjana (Kragujevac, Serbia , 2011)[more][less]
Abstract: This doctoral dissertation belongs to the Spectral theory of finite and infinite graphs, which joins elements of Graph theory and Linear algebra. The dissertation, beside Preface and References with 24 items, consists of four chapters divided in sections and Appendix. In Chapter 1 some results on the reduced energy of graphs are given. All connected graphs whose reduced energy does not exceed 3 are described. In Chapter 2 all finite and infinite graphs with seven nonzero eigenvalues are determined. Some results on integral graphs are given in Chapter 3. Finally, Chapter 4 contains some results on symmetric double starlike trees. The definitions of starlike tree and double starlike tree are given and we proved that there exist no two cospectral nonisomorphic symmetric double starlike trees. URI: http://hdl.handle.net/123456789/1879 Files in this item: 1
dokdis.pdf ( 713.4Kb ) 
Matić, Dragan (Beograd , 2013)[more][less]
Abstract: In this work some actual combinatorial optimization problems are investigated. Several di erent methods are suggested for solving the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions (q ≥ 2), maximum set splitting problem and pary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving pary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various elds of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of nding maximally balanced connected partition in graph and nding maximum splitting of the set can be successfully used in course organization, which is veri ed on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scienti c contributions in the elds of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science. URI: http://hdl.handle.net/123456789/4229 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) 
Matić, Dragan (Beograd , 2013)[more][less]
Abstract: In this work some actual combinatorial optimization problems are investigated. Several di erent methods are suggested for solving the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions (q ≥ 2), maximum set splitting problem and pary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving pary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various elds of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of nding maximally balanced connected partition in graph and nding maximum splitting of the set can be successfully used in course organization, which is veri ed on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scienti c contributions in the elds of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science. URI: http://hdl.handle.net/123456789/3050 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) 
Todorčević, Stevo (Belgrade)[more][less]
Abstract: The thesis consists of four chapters and one appendix. The relation between trees and ordering types, especially the relation between treesubtree and the typesubtype are considered in Chapter 1. By using Jensens’s principle, Aronszajn’s tree which does not contain any Aronszajn’s subtree and Cantor’s subtree are constructed. Moreover, it is shown that in the model ZFC+GCH each ω_2 Aronszajn’s tree contains Aronszajn’s and Cantor’s subtree. In the first part of Chapter 2 the problem of the existence of Boolean algebras which have nontrivial automorphisms and endomorptisms are studied. It is shown that for each cardinal k, k>ω, there are exactly 2^k types of isomorphic Boolean algebras without nontrivial automorphisms. In the second part of that chapter the problem of isomorphism and automorhism of ω_1trees is studied. It is shown that there are 2^ω1 types of isomorphic total rigid Aronszajn’s trees, so one Aronszajn’s tree does not have any nontrivial automorphism. Several problems of the partition relations of cardinal numbers are solved in Chapter 3. The appendix contains the proof of the property that in ZFC the σdense partial ordered set of power ω_1 does not exist. It is shown that in ZFC there is not any linearly ordered topological space with weight less or equal ω_1 which satisfies Kurepa’s generalization of the notion of separable topological space. It is also shown that if ¬ω Kurepa’s hypothesis + Martin’s axiom + ¬Continuum hypothesis is assumed, then each perfect normal non  Arhimedian space whose weight is ω1 is measurable. URI: http://hdl.handle.net/123456789/316 Files in this item: 1
phdStevoTodorcevic.pdf ( 18.19Mb ) 
Dragović, Vladimir (Beograd , 1992)[more][less]

Borisavljević, Mirjana (Beograd , 1997)[more][less]

Bakić, Radoš (Belgrade)[more][less]

Mijajlović, Ivana (London)[more][less]

Pavlović, Aleksandar (Novi Sad)[more][less]
URI: http://hdl.handle.net/123456789/295 Files in this item: 1
PhdAleksandarPavlovic.pdf ( 7.226Mb ) 
Pogany, Tibor (Belgrade)[more][less]

Todorović, Petar (Belgrade , 1961)[more][less]

Ikodinović, Nebojša (Kragujevac)[more][less]
Abstract: The thesis is devoted to logics which are applicable in different areas of mathematics (such as topology and probability) and computer sciences (reasoning with uncertainty). Namely, some extensions of the classical logic, which are either modeltheoretical or nonclassical, are studied. The thesis consists of three chapters: an introductory chapter and two main parts (Chapter 2 and Chapter 3). In the introductory chapter of the thesis the wellknown notions and properties from extensions of the first order logic and nonclassical logics are presented. Chapter 2 of the thesis is related to logics for topological structures, particularly, topological class spaces (topologies on proper classes). One infinite logic with new quantifiers added is considered as the corresponding logic. Methods of constructing models, which can be useful for many others similar logics, are used to prove the completeness theorem. A number of probabilistic logic suitable for reasoning with uncertainty are investigated in Chapter 3. Especially, some ways of incorporation into the realm of logic conditional probability understood in different ways (in the sense of Kolmogorov or De Finnety) are given. For all these logics the corresponding axiomatizations are given and the completeness for each of them is proved. The decidability for all these logics is discussed too. URI: http://hdl.handle.net/123456789/194 Files in this item: 1
phdNebojsaIkodinovic.pdf ( 3.008Mb )