Browsing Doctoral Dissertations by Title
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Koledin, Tamara (Beograd , 2013)[more][less]
Abstract: Spectral graph theory is a branch of mathematics that emerged more than sixty years ago, and since then has been continuously developing. Its importance is re ected in many interesting and remarkable applications, esspecially in chemistry, physics, computer sciences and other. Other areas of mathematics, like linear algebra and matrix theory have an important role in spectral graph theory. There are many di erent matrix representations of a given graph. The ones that have been studied the most are the adjacency matrix and the Laplace matrix, but also the Seidel matrix and the so-called signless Laplace matrix. Basically, the spectral graph theory establishes the connection between some structrural properties of a graph and the algebraic properties of its matrix, and considers structural properties that can be described using the properties of the eigenvalues of its matrix. Systematized former results from this vast eld of algebraic graph theory can be found in the following monographs: [20], [21], [23] i [58]. This thesis contains original results obtained in several sub elds of the spectral graph theory. Those results are presented within three chapters. Each chapter is divided into sections, and some sections into subsections. At the beginning of each chapter (in an appropriate sections), we formulate the problem considered within it, and present the existing results related to this problem, that are necessary for further considerations. All other sections contain only original results. Those results can also be found in the following papers: [3], [4], [47], [48], [49], [50], [51] and [52]. In the rst chapter we consider the second largest eigenvalue of a regular graph. There are many results concerning graphs whose second largest eigenvalue is upper bounded by some (relatively small) constant. The second largest eigenvalue plays an important role in determining the structure of regular graphs. There is a known characterization of regular graphs with only one positive eigenvalue (see [20]), and regular graphs with the property 2 ≤ 1 have also been considered (see [64]). Within this thesis we extend the results given in [64], and we also present some general results concerning the relations between some structural and spectral properties of regular triangle-free graphs. Connected regular graphs with small number of distinct eigenvalues have been extensively studied, since they usually have an interesting (combinatorial) struc- ture. Van Dam and Spence considered the problem of determining the structure of connected regular graphs with exactly four distinct eigenvalues, and they achieved important results presented in papers [27] and [32]. All connected regular bipar- tite graphs with exactly four distinct eigenvalues are characterized as the incidence graphs of balanced incomplete block designs (see monograph [20]). There are also results concerning regular bipartite graphs with exactly ve distinct eigenvalues (see [33]). In this thesis, in the second chapter, we consider regular bipartite graphs with three distinct non-negative eigenvalues, and also quadrangle-free regular bipartite graphs. Besides some general results similar to those given in the rst chapter, but this time for bipartite graphs, we also present results concerning the relations between regular bipartite graphs and certain kinds of block designs. In the third chapter we consider the so-called nested graphs and their signless Laplace matrix. Nested graphs play an important role in the research concerning graphs with maximal index, in terms of the adjacency matrix and in terms of the signless Laplace matrix. It is a known fact that a graph with maximal index, or maximal Q-index, of given order and size, must be nested graph (see [7] and [22]). Here we consider bipartite nested graphs (the so-called double nested graphs). We also present results concerning double nested graphs that are similar to the existing results concerning their non-bipartite counterparts. There are no many results con- cerning the second largest eigenvalue of the signless Laplace matrix of a graph (see, for example, [6] or [25]). That is why we consider the relations between the structure of nested graphs and the second largest eigenvalue (but also some URI: http://hdl.handle.net/123456789/3049 Files in this item: 1
Koledin_Tamara.pdf ( 7.477Mb ) -
Zolić, Arif (Belgrade)[more][less]
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Protić, Ljubomir (Belgrade)[more][less]
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Kočinac, Ljubiša (Belgrade , 1983)[more][less]
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Pap, Endre (Novi Sad)[more][less]
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Perović, Aleksandar (Belgrade)[more][less]
Abstract: The interpretation method is a characteristic common for all results from this thesis. The thesis consists of five chapters and two appendices. A brief overview of the contents of the thesis and the obtained results are presented in Chapter 1. Logical background and the well-known notions the basic notions, definitions and properties from forcing are given in the appendices of the thesis. An elementary proof of equivalence between Cohen forcing and forcing with propositional Lindenbaum algebras is presented in Chapter 2. Dense embedding and the interpretation method are used in that proof. A complete axiomatization of the notion of qualitative probability is presented in Chapter 3. Probabilistic logic LPP_2 LPP_2^FR(n) and LPP^S are extended with the qualitative probability operator π. Several formal techniques as infinite rules, elimination of quantifiers and interpretation method (implicitly), are used to prove the extended completeness theorem and decidability for these logics. In Chapter 4 of the thesis a complete axiomatization of the logic with polynomial weight formulas is presented and the extended completeness theorem is proved. Applications of the interpretation method are given. By using that method the compactness theorem for the non-archimedean valued probabilistic logics is proved in Chapter 5. URI: http://hdl.handle.net/123456789/100 Files in this item: 1
phdAleksandarPerovic.pdf ( 700.0Kb ) -
Laban, Miloš (Belgrade , 1980)[more][less]
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Janković, Svetlana (Belgrade)[more][less]
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Karadžić, Lazar (Belgrade)[more][less]
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Petrović, Vojislav (Novi Sad)[more][less]
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Janković, Aleksandra (Belgrade , 1989)[more][less]
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Ušćumlić, Momčilo (Belgrade , 1965)[more][less]
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Radenović, Stojan (Belgrade)[more][less]
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Janeva, Biljana (Skopje)[more][less]
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Stojanović, Miroslava (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/350 Files in this item: 1
phdMiroslavaStojanovic.pdf ( 2.145Mb ) -
Ćetković, Simon (Belgrade)[more][less]
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Kostić, Aleksandra (Beograd , 2021)[more][less]
Abstract: This dissertation examines simplicial complexes associated with cyclotomic po-lynomials and irreducible characters of finite solvable groups. In the process of analysis ofthe associated objects special attention is paid to the noncommutativity of the examinedstructures.A collection of simplicial complexes can be associated to an algebraic object such as acyclotomic polynomial. In most cases, the homotopy type of associated simplicial complexesgives us complete information about the coefficients of the cyclotomic polynomial. The onlyexceptions are cyclotomic polynomials whose degree is a product of three different primenumbers and this case is the focus of research in this doctoral dissertation. When it ispossible, the homotopy type of a simplicial complex associated with the polynomialΦpqr(x),wherep,qandrare different prime numbers, is determined by using the discrete Morsetheory. However, in special cases, the simplicial complexes associated with the polynomialΦpqr(x)have a noncommutative fundamental group, thus providing a new noncommutativeinvariant of this type of polynomial. Complex presentations that appear as presentations ofthe fundamental groups of associated simplicial complexes are analyzed using Fox’s calculus.This thesis also focus on the study of simplicial complexes associated to a set of irreduciblecharacters of a finite solvable group. Two types of simplicial complexes are attached to aset of irreducible characters of a finite solvable group — character degree complex and primedivisor complex. The examination of the fundamental group of these types of simplicial com-plexes provides better understanding of the structure of the irreducible characters of finitesolvable groups. URI: http://hdl.handle.net/123456789/5096 Files in this item: 1
Teza-Aleksandra_Kostic.pdf ( 1.009Mb ) -
Peruničić, Predrag (Belgrade , 1984)[more][less]
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Gopčević, Špiro (Beograd , 2007)[more][less]
Abstract: U radu je prikazana nelinearna analiza konstrukcija sa kablovima. Formulisan je odgovaraju´ci matematiˇcki model problema. Pretpostavljeno je da je materijal konstrukcije izotropan i linearno-elastiˇcan. Primenom korigovane Lagrange-ove formulacije i nelinearnog polja pomeranja popreˇcnog preseka, izvedene su linearizovane inkrementalne jednaˇcine ravnoteˇze elementa. Na osnovu analitiˇckog reˇsenja za lanˇcanicu, a za razliˇcite poˇcetne pretpostavke, izvedeni su konaˇcni elementi za plitku i duboku lanˇcanicu. Ovi konaˇcni elementi su koriˇs´ceni za aproksimaciju kablova u konstrukcijama. Kao ˇsto sledi iz samog naziva, kablovi u konstrukcijama sa kablovima obiˇcno su povezani sa drugim tipovima elemenata, te je osim modeliranja kablova, urad¯eno i modeliranje tankozidnih i grednih nosaˇca. Izvedeni konaˇcni elementi za gredne nosaˇce, takod¯e, mogu da se upotrebljavaju za aproksimaciju kablova u konstrukcijama sa kablovima. U sluˇcaju nelinearne statiˇcke analize usvojen je inkrementalno-iterativni postupak za reˇsavanje sistema nelinearnih jednaˇcina, u varijanti Newton-Raphson-ovog i/ili modifikovanog Newton-Raphsonovog postupka. U sluˇcaju nelinearne dinamiˇcke analize usvojena je direktna numeriˇcka integracija, u varijanti Newmark-ovog postupka, u kombinaciji sa inkrementalno-iterativnom analizom u vremenskim koracima. Urad¯ena je objektno orijentisana analiza matematiˇckog modela i dobijen je objektno-orijentisani model podataka zasnovan na objektno orijentisanoj paradigmi. Na osnovu matematiˇckog modela i objektno-orijentisanog modela podataka, urad¯en je raˇcunarski program u jeziku C++. Dobijeni program omogu´cava linearnu i nelinearnu analizu konstrukcija sa kablovima, usled dejstva statiˇckog i dinamiˇckog optere´cenja. Taˇcnost raˇcunarskog programa proverena je kroz test primere dostupne u literaturi. URI: http://hdl.handle.net/123456789/3811 Files in this item: 1
070Doktorat.pdf ( 3.216Mb ) -
Bjelica, Momčilo (Beograd , 1990)[more][less]