Auflistung Mathematical Sciences nach Titel
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Majstorović, Ivana (Beograd , 2020)[more][less]
URI: http://hdl.handle.net/123456789/5081 Dateien zu dieser Ressource: 1
MajstorovicIvana.pdf ( 949.7Kb ) -
Cvetković, Dragoš (Belgrade , 1987)[more][less]
URI: http://hdl.handle.net/123456789/460 Dateien zu dieser Ressource: 1
book001DragosCvetkovic.pdf ( 15.14Mb ) -
Jelić Milutinović, Marija (Beograd , 2021)[more][less]
Zusammenfassung: In this dissertation we examine several important objects and concepts in combinatorialtopology, using both combinatorial and topological methods.The matching complexM(G) of a graphGis the complex whose vertex set is the setof all edges ofG, and whose faces are given by sets of pairwise disjoint edges. These com-plexes appear in many areas of mathematics. Our first approach to these complexes is newand structural - we give complete classification of all pairs (G,M(G)) for whichM(G) is ahomology manifold, with or without boundary. Our second approach focuses on determiningthe homotopy type or connectivity of matching complexes of several classes of graphs. Weuse a tool from discrete Morse theory called the Matching Tree Algorithm and inductiveconstructions of homotopy type.Two other complexes of interest are unavoidable complexes and threshold complexes.Simplicial complexK⊆2[n]is calledr-unavoidable if for each partitionA1t···tAr= [n] atleast one of the setsAiis inK. Inspired by the role of unavoidable complexes in the Tverbergtype theorems and Gromov-Blagojevi ́c-Frick-Ziegler reduction, we begin a systematic studyof their combinatorial properties. We investigate relations between unavoidable and thre-shold complexes. The main goal is to find unavoidable complexes which are unavoidable fordeeper reasons than containment of an unavoidable threshold complex. Our main examplesare constructed as joins of self-dual minimal triangulations ofRP2,CP2,HP2, and joins ofRamsey complex.The dissertation contains as well an application of the important “configuration space -test map” method. First, we prove a cohomological generalization of Dold’s theorem fromequivariant topology. Then we apply it to Yang’s case of Knaster’s problem, and obtain anew simpler proof. Also, we slightly improve few other cases of Knaster’s problem. URI: http://hdl.handle.net/123456789/5184 Dateien zu dieser Ressource: 1
Marija_Jelic_Milutinovic.pdf ( 5.212Mb ) -
Stojadinović, Tanja (Beograd , 2013)[more][less]
Zusammenfassung: Multiplication and comultiplication, which de ne the structure of a Hopf algebra, can naturally be introduced over many classes of combinatorial objects. Among such Hopf algebras are well-known examples of Hopf algebras of posets, permutations, trees, graphs. Many classical combinatorial invariants, such as M obius function of poset, the chromatic polynomial of graphs, the generalized Dehn-Sommerville relations and other, are derived from the corresponding Hopf algebra. Theory of combinatorial Hopf algebras is developed by Aguiar, Bergerone and Sottille in the paper from 2003. The terminal objects in the category of combinatorial Hopf algebras are algebras of quasisymmetric and symmetric functions. These functions appear as generating functions in combinatorics. The subject of study in this thesis is the combinatorial Hopf algebra of hypergraphs and its subalgebras of building sets and clutters. These algebras appear in di erent combinatorial problems, such as colorings of hypergraphs, partitions of simplicial complexes and combinatorics of simple polytopes. The structural connections among these algebras and among their odd subalgebras are derived. By applying the character theory, a method for obtaining interesting numerical identities is presented. The generalized Dehn-Sommerville relations for ag f-vectors of eulerian posets are proven by Bayer and Billera. These relations are de ned in an arbitrary combinatorial Hopf algebra and they determine its odd subalgebra. In this thesis, the generalized Dehn-Sommerville relations for the combinatorial Hopf algebra of hypergraphs are solved. By analogy with Rota's Hopf algebra of posets, the eulerian subalgebra of the Hopf algebra of hypergraphs is de ned. The combinatorial characterization of eulerian hypergraphs, which depends on the nerve of the underlying clutter, is obtained. In this way we obtain a class of solutions of the generalized Dehn-Sommerviller relations for hypergraphs. These results are applied on the Hopf algebra of simplicial complexes. URI: http://hdl.handle.net/123456789/4306 Dateien zu dieser Ressource: 1
phdTanjaStojadinovic.pdf ( 13.95Mb ) -
Stojadinović, Tanja (Univerzitet u Beogradu , 2014)[more][less]
Zusammenfassung: Multiplication and comultiplication, which de ne the structure of a Hopf algebra, can naturally be introduced over many classes of combinatorial objects. Among such Hopf algebras are well-known examples of Hopf algebras of posets, permutations, trees, graphs. Many classical combinatorial invariants, such as M obius function of poset, the chromatic polynomial of graphs, the generalized Dehn-Sommerville relations and other, are derived from the corresponding Hopf algebra. Theory of combinatorial Hopf algebras is developed by Aguiar, Bergerone and Sottille in the paper from 2003. The terminal objects in the category of combinatorial Hopf al- gebras are algebras of quasisymmetric and symmetric functions. These functions appear as generating functions in combinatorics. The subject of study in this thesis is the combinatorial Hopf algebra of hyper- graphs and its subalgebras of building sets and clutters. These algebras appear in di erent combinatorial problems, such as colorings of hypergraphs, partitions of sim- plicial complexes and combinatorics of simple polytopes. The structural connections among these algebras and among their odd subalgebras are derived. By applying the character theory, a method for obtaining interesting numerical identities is pre- sented. The generalized Dehn-Sommerville relations for ag f-vectors of eulerian posets are proven by Bayer and Billera. These relations are de ned in an arbitrary com- binatorial Hopf algebra and they determine its odd subalgebra. In this thesis, the generalized Dehn-Sommerville relations for the combinatorial Hopf algebra of hy- pergraphs are solved. By analogy with Rota's Hopf algebra of posets, the eulerian subalgebra of the Hopf algebra of hypergraphs is de ned. The combinatorial char- acterization of eulerian hypergraphs, which depends on the nerve of the underlying clutter, is obtained. In this way we obtain a class of solutions of the generalized Dehn-Sommerviller relations for hypergraphs. These results are applied on the Hopf algebra of simplicial complexes. URI: http://hdl.handle.net/123456789/3745 Dateien zu dieser Ressource: 1
phdTanjaStojadinovic.pdf ( 13.95Mb ) -
Telebak, Vladimir (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
URI: http://hdl.handle.net/123456789/1824 Dateien zu dieser Ressource: 1
msVladimirTelebak.pdf ( 744.5Kb ) -
Todić, Bojana (Beograd , 2024)[more][less]
Zusammenfassung: This dissertation deals with the coupon collector problem, which in its simplest (classical) form can be formulated as follows: A collector wants to collect a set of n distinct coupons, by buying a single coupon each day. The random variable of interest is the waiting time until the collection is completed. The goal of the dissertation is to propose and analyze three new generalizations of the classical coupon collector problem obtained by introducing additional coupons with special purposes into the set of n standard coupons. The first two chapters are devoted to the results on the classical coupon collector problem and the known generalizations obtained by introducing additional coupons into the coupon set ([1], [2], [39], [54]). New results are presented in chapters 3,4, and 5. The third chapter of the dissertation is dedicated to the case where, in addition to the standard coupons, the coupon set consists of a null coupon (which can be drawn, but does not belong to any collection), and an additional universal coupon, that can replace any standard coupon. For the case of equal probabilities of standard coupons, the asymptotic behavior (as n → ∞) of the expectated value and variance of the waiting time for a fixed size subcollection of a collection of coupons is obtained when one or both probabilities of additional coupons are fixed, and the remaining coupons have equal small probabilities. These results, published in [27], generalize part of the results in [2]. The same problem is analyzed using a Markov chain approach, which led to the determination of the fundamental matrix and some related features of the collection process (probability that the coupon collection process ends in a certin way). These results are contained in the paper [24]. For the case of unequal probabilities of standard coupons, a class of bounds is derived for the first and second moments of the waiting time until the end of the experiment by using majorization techniques and refining the bounds proposed in [51]. The quality of the proposed bounds is tested in numerical experiments, and the specific bounds from the class with the most desirable properties are given. These results are published in [26]. The fourth chapter of the dissertation deals with the generalization in which the additional coupon (so called, penalty coupon) interferes with the collection of standard coupons in the sense that the collection process ends when the absolute difference between the number of collected standard coupons and the number of collected penalty coupons is equal to n. This generalization can be seen as a special case of the random walk with two absorbing barriers. The distribution and a simple upper bound on the first moment of the corresponding waiting time are determined by combinatorial considerations. The application of the Markov chain approach led to obtaining the fundamental matrix. These results are published in [53]. In the fifth chapter of the dissertation another additional coupon (so called reset coupon) is introduced, which acts as a reset button, in the sense that the set of coupons drawn up to time (day) t becomes empty if the reset coupon is drawn on day t+1. In the case of unequal probabilities of standard coupons, the distribution of the corresponding waiting time is obtained by combinatorial considerations. For the case of equal probabilities of obtaining standard coupons, For the case of equal probabilities, applying the first step analysis for the correspondingly constructed Markov chains led to the expressions for the expected waiting time and its simple form in terms of the beta function. These results are used for analysing the asymptotic behavior (when the size of the collection tends to infinity) of the expected waiting time, taking into account possible values of the probability of obtaining a reset coupon. These results are published in [25]. Setting the probabilities of the additional coupons to zero, all three generalizations of the coupon collector problem defined and analyzed in this dissertation as well as the obtained results reduce to the corresponding results for the classical coupon collector problem. URI: http://hdl.handle.net/123456789/5677 Dateien zu dieser Ressource: 1
Todic_Bojana_disertacija.pdf ( 1.004Mb ) -
Muminović, Muhamed (Savez astronomskih društava BiH, ASTRONOMSKA OPSERVATORIJA, Sarajevo , 1985)[more][less]
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Kršljanin, V.; Dimitrijević, M.; Vince, I.; Vujnović, V.; Jankov, S.; Teleki, Dj.; Čabrić, N.; Protić - Benišek, V.; Janković, N.; Protić, M.; Arsenijević, J.; Prosen, M.; Djokić, M. (ASTRONOMSKA OPSERVATORIJA U BEOGRADU i ASTRONOMSKO DRUŠTVO 'Rudjer Bošković' , 1986)[more][less]
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Bačević, Stefan (Beograd , 2017)[more][less]
URI: http://hdl.handle.net/123456789/4653 Dateien zu dieser Ressource: 1
masBacevicStefan.pdf ( 1.686Mb ) -
Đurđević, Dragan (Beograd , 2013)[more][less]
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Stanković, Danijela (Beograd , 2018)[more][less]
URI: http://hdl.handle.net/123456789/4693 Dateien zu dieser Ressource: 1
masterStankovicDanijela.pdf ( 2.355Mb ) -
Savović, Vjera (Beograd , 2023)[more][less]
URI: http://hdl.handle.net/123456789/5612 Dateien zu dieser Ressource: 1
v1_masterVjeraSavovic.pdf ( 655.3Kb ) -
Karamata, Jovan (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/443 Dateien zu dieser Ressource: 1
JovanKaramataKompleksanBroj.pdf ( 45.35Mb ) -
Urošević, Marina (Beograd , 2022)[more][less]
URI: http://hdl.handle.net/123456789/5448 Dateien zu dieser Ressource: 1
UrosevicMarina.pdf ( 465.5Kb ) -
Lazović, Milena (Beograd , 2017)[more][less]
URI: http://hdl.handle.net/123456789/4521 Dateien zu dieser Ressource: 1
masLazovicMilena.pdf ( 1.788Mb ) -
Babić, Sladjana (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2009)[more][less]
URI: http://hdl.handle.net/123456789/1877 Dateien zu dieser Ressource: 1
Magistarski_rad.pdf ( 3.575Mb ) -
Avalić, Dijana (Beograd , 2015)[more][less]
URI: http://hdl.handle.net/123456789/4241 Dateien zu dieser Ressource: 1
Avalic_Dijana.pdf ( 1.721Mb ) -
Đurica, Marina (Beograd , 2017)[more][less]
URI: http://hdl.handle.net/123456789/4677 Dateien zu dieser Ressource: 1
masDjuricaMarina.pdf ( 724.1Kb ) -
Marković, Sima (, 2012)[more][less]