Browsing Mathematics by Title

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 ) 
Ognjanović, Zoran (Kragujevac)[more][less]
Abstract: The thesis consists of seven chapters and two appendixes. The Chapter 1 and the appendixes contain known notions and properties from probability logics. In Chapter 2 some propositional probability logics are introduced and their languages, models, satisfiability relations, and (in)finitary axiomatic systems are given. Object languages are countable, formulas are finite, while only proofs are allowed to be infinite. The considered languages are obtained by adding unary probabilistic operators of the form P≥s. Decidability of the logics is proved. In Chapter 3 some first order probability logics are considered while in Chapter 4 new types of probability operators are introduced. The new operators are suitable for describing events in discrete sample spaces. It is shown that they are not definable in languages of probability logics that have been used so far. A propositional and a firstorder logic for reasoning about discrete linear time and finitely additive probability are given in Chapter 5. Sound and complete infinitary axiomatizations for the logics are provided as well. In Chapter 6 a probabilistic extension of modal logic is studied and it is shown that those logics are closely related, but that modal necessity is a stronger notion than probability necessity. In Chapter 7 decidability of these logics is shown by reducing the corresponding satisfiability problem to the linear programming problem. Finally, two automated theorems provers based on that idea are described. URI: http://hdl.handle.net/123456789/197 Files in this item: 1
phdZoranOgnjanovic.pdf ( 1.259Mb ) 
Shkheam, Abejela (, 2013)[more][less]
Abstract: This thesis has been written under the supervision of my mentor, Prof. dr. Milo s Arsenovi c at the University of Belgrade academic, and my comentor dr. Vladimir Bo zin in year 2013. The thesis consists of three chapters. In the rst chapter we start from de nition of harmonic functions (by mean value property) and give some of their properties. This leads to a brief discussion of homogeneous harmonic polynomials, and we also introduce subharmonic functions and subharmonic behaviour, which we need later. In the second chapter we present a simple derivation of the explicit formula for the harmonic Bergman reproducing kernel on the ball in euclidean space and give a proof that the harmonic Bergman projection is Lp bounded, for 1 < p < 1, we furthermore discuss duality results. We then extend some of our previous discussion to the weighted Bergman spaces. In the last chapter, we investigate the Bergman space for harmonic functions bp, 0 < p < 1 on RnnZn. In the planar case we prove that bp 6= f0g for all 0 < p < 1. Finally we prove the main result of this thesis bq bp for n=(k + 1) q < p < n=k, (k = 1; 2; :::). This chapter is based mainly on the published paper [44]. M. Arsenovi c, D. Ke cki c,[5] gave analogous results for analytic functions in the planar case. In the plane the logarithmic function log jxj, plays a central role because it makes a di erence between analytic and harmonic case, but in the space the function jxj2n; n > 2 hints at the contrast between harmonic function in the plane and in higher dimensions. URI: http://hdl.handle.net/123456789/3053 Files in this item: 1
phd_Shkheam_Abejela.pdf ( 650.6Kb )