Browsing Mathematics by Title
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Vučemilović, Ante (Belgrade)[more][less]
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Cerović, Blagoje (Novi Sad , 1982)[more][less]
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Crvenković, Siniša (Novi Sad , 1981)[more][less]
Abstract: Teorija semigrupa razvija se kao samostalna °blast savremene algebre, Predmet izu6avanja teorije semigrupa su razne kiase semigrupa tj. semigrupe koje zadovoljavaju dati uslov. U ovom radu razmatramo semigrupe iz nekih podklasa kiase regularnih semigrupa. Pojam regularnosti, koji je uveo J. von Neumann [31] za prstene, su Thierrin i BarHep preneli u teoriju semigrupa 6to se pokazalo zna6ajnim za razvoj teorije semigrupa umAte. Ovde se posebno ispituje jedna podklasa kiase kompletno regularnih semigrupa tzv. klasa (m,n)*-anti-inverznih semigrupa. Ova klasa obuhvata klasu anti-inverznih semigrupa ill Pojam bazisne kiase, neke klase semigrupa, uveo je E.C. JThnHH [25]. U radu odredjujemo bazisne kiase za razne kiase semigrupa. Zna6ajnu klasu semigrupa 6ine polumr0e. P.M. Cohn [9] i C. Pe6aHe su 1965. godine pokazali da je svaka algebra podalgebra neke semigrupe. U Glavi IV opisujemo klasu algebri koje su podalgebre polumrea. U Glavi I su navedeni elementarni pojmovi o semigrupama, grupama, algebrama, idealima, kongruencijama, itd. Dati Virtual Library of Faculty of Mathematics - University of Belgrade elibrary.matf.bg.ac.rs ii su dokazi nekih teorema koje se koriste u radu. Ovaj materijal uzet je iz [7] i [22]. Takodje, dat je dokaz G. upone za teoremu Cohn-Pe6aHe. U Glavi II ispituju se (m,n)*-anti-inverzne semigrupe. Materijal ove glave preuzet je iz [ 61, [11] i [12]. U ta6ki 2. date su neke dekompozicije (m,n)*-anti-inverznih semigrupa. Teorema 2.3. glavni je rezultat ove glave. Green-ove relacije razmatraju se u ta6ki 3. Dobija se niz karakterizaci - ja semigrupa iz klase m,n . Na kraju Glave II navedena su tvrdjenja Eiji dokazi su izostavljeni jer su sli6ni dokazima teorema u [ 21. U Glavi III ispituju se bazisne klase raznih klasa semigrupa. Dat je algoritam kojim odredjujemo bazisnu klasu bilo koje klase (m,n)*-anti-inverznih semigrupa. Primeri bazisnih klasa za razne semigrupe dati su u ta6ki 2. Materim, n jal za take 1. i 2. uzet je iz [121. U ta6ki 3. razmatraju se QS* (OS ) semigrupe tj. semigrupe nje sve prave podsemi - m,n m,n grupe pripadaju klasi m,n (Sm,n ). Teoremom 3.1. data je karakterizacija semigrupa klase QS*m,n (QS m,n ). Problem egzistencije bazisne klase semigrupa ije sve prave podsemigrupe zadovoljavaju uslov oblika (Vx)(By)4)(x,y) re§en je u ta6ki 4. Na kraju 4. data je nekoliko primera. Materijal iz ta6aka 3. i 4. ovde je prvi put izloen. U Glavi IV opisane su podalgebre polumr0a. Potreban i dovoljan uslov da neka algebra bude podalgebra polumree dat je u taCki 1. Lema 1.3. je kljufta lema u dokazu teoreme 1.1. Virtual Library of Faculty of Mathematics - University of Belgrade elibrary.matf.bg.ac.rs iii Dokaz ove leme izvodi se koristedi pojam transformacije U tadki 2. navedeni su neki specijalni sludajevi koji su neposredna posledica teoreme 1.1. Materijal za ovu glavu uzet je iz [18]. Literatura koja je korigdena u ovom radu navedena je na kraju i 6ine je 44 bibliografske jedinice. Dr Stojan Bogdanovid svojim idejama i savetima pornogao mi je pri izradi ovog rada zbog 6eqa mu dugujem trajnu zahvalnost. Akademik profesor (op(- 11 HynoHa velikodugno je pristao na saradnju sa autorom ovog rada. Zahvaljujem se profesoru 6to je prihvatio moju saradnju i omogudio mi da rezultato zajedni6kocr rada izlo2im u Glavi IV. Profesor Svetozar Milid prihvatio se da bude mentor pri izradi ove disertacije. Imam prijatnu du2nost da se zahvalim profesoru Milidu za nesebi6nu pa2nju koju posvedije mom radu. URI: http://hdl.handle.net/123456789/4094 Files in this item: 1
Neke_klase_semigrupa.PDF ( 10.42Mb ) -
Crvenković, Siniša (Novi Sad , 1981)[more][less]
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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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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 )