Browsing Doctoral Dissertations by Title
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Takači, Arpad (Novi Sad , 1981)[more][less]
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Mitić, Ljubiša (Belgrade)[more][less]
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Nikić, Mioljub (Belgrade)[more][less]
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Demčenko, Vasilije (Belgrade , 1924)[more][less]
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Stojanović, Rastko (None , 1956)[more][less]
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Vujičić, Veljko (Belgrade , 1961)[more][less]
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Radosavljević, Jovan (Beograd , 2023)[more][less]
Abstract: Graph G = (V,E) is an ordered pair of set of nodes V and branches E. Order graph G is the number of nodes |V |, and its size is the number of branches |E|. Knots u, v ∈ V are adjacent if there is a branch uv ∈ E between them. Distance dist(u, v) nodes u and v G is the length of the shortest path from u to v. The diameter of the graph G is the largest distance dist(u, v) let two nodes in, v. They are discussed in the dissertation graphs of diameter 2. Intuitively, the notion that graphs are dia- meters 2 simple structures; however, they are known to be asymptotically close all graphs of diameter 2. That is why a narrower class is interesting — class D2C of critical graphs of diameter 2, i.e. graphs where the removal of any branches leads to an increase in diameter. In addition, a narrower class of pri- mitive D2C (PD2C) graphs, i.e. D2C graphs that do not have two nodes with the same set of neighbors. In the introductory chapter 2, the basic concepts, algorithms and dings used in the dissertation. They are presented in the following chapters original results regarding diameter graphs 2. Chapter 3 describes the procedure for obtaining a list of D2C graphs of order up to 13. With built-in parallelization, the creation of a list of D2C graphs of order up to 13 it lasted a month. This was a step forward, because previously there was a spi- around all graphs of diameter 2 lines up to 10. The obtained results were used for testing several known hypotheses about graphs of diameter 2. In chapter 4 it is shown that for every m ⩾ 3 a D2C graph containing cli- a ku of size m must have at least 2m nodes. At the same time, with accuracy up to isomorphism, there is exactly one graph of size 2m that contains a clique of characters m. Chapter 5 discusses PD2C graphs with the smallest number of branches. From list of all PD2C graphs of order n ⩽ 13 are selected PD2C graphs of size at most 2n − 4. Only three of the isolated graphs are of size 2n − 5, which is in accordance with the statement of the Erdes-Renji theorem about the lower bound for the size graphs of diameter 2 that do not contain a node adjacent to all other nodes (that limit is 2n − 5). PD2C graphs of size 2n − 4 rows up to 13 sorted are in three groups: • The first group belongs to the Z family, defined in the dissertation, which for each n ⩾ 6 contains exactly one PD2C graph of order n of size 2n − 4. • The second group consists of seven Hamiltonian PD2C graphs of order at most 9 of size 2n−4. In the dissertation it was proved that there is no such Hamil- tone graph of order greater than 11, i.e. that the seven graphs found are the only ones Hamiltonian PD2C graphs of size 2n − 4. • The third group consists of a unique graph that does not belong to any of the first two groups. Based on these results, the hypothesis was formulated that all PD2C graphs re- that n ⩾ 10 and sizes 2n − 4 belong to the family Z. Keywords: graphs, critical graphs of diameter 2, primitive graph- You Scientific field: Computing and informatics Narrower scientific field: Graph theory UDC number: 004.415.5(519.1 URI: http://hdl.handle.net/123456789/5594 Files in this item: 1
disertacijaJovanRadosavljevic.pdf ( 746.0Kb ) -
Blažić, Novica (Belgrade)[more][less]
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Krstić, Sava (Belgrade)[more][less]
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Stević, Stevo (Belgrade , 2001)[more][less]
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Glišić, Zoran (Belgrade)[more][less]
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Stojaković, Zoran (Belgrade)[more][less]
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Mićić, Vladimir (Belgrade , 1973)[more][less]
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Stanojević, Vera (Belgrade , 1983)[more][less]
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Šili, Endre (Belgrade , 1985)[more][less]
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Đorđević, Vladan (Belgrade , 1966)[more][less]
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Petrović, Mihailo (Paris , 1894)[more][less]
URI: http://hdl.handle.net/123456789/3737 Files in this item: 1
Mik_Alas_Pariz_1894_high.pdf ( 23.25Mb ) -
Ababoub, Ali (Belgrade , 2013)[more][less]
Abstract: This thesis has been written under the supervision of my mentor Prof. Miodrag Mateljevi c, and my co-mentor dr. Vladimir Bo zin at the University of Belgrade in the academic year 2012-2013. The topic of this thesis is Complex analysis related with geometric function theory, more precisely the theory of quasiconformal mappings in the Euclidean n-dimensional space. For good survey of the eld, see F. W. Gehring [20] in the handbook of K uhnau [33] which also contains many other surveys on quasiconformal mappings and related topics. The main source in this dissertation is J. V ais al a [67]. The thesis is divided into three chapters. Chapter 1 is divided into 5 sections. In this chapter, we focus on quasiconformal mappings in Rn and discuss various equivalent de nitions. We give The Modulus of family of curves in the rst section, geometric de nition of quasiconformal space mappings in second section, analytic de nition of quasiconformal space mappings in third section, equivalence of the de nitions in fourth section, and the Beltrami equation in fth section. Chapter 2 is divided into 5 sections. We begin by generalizing the class of Lip ( ), 0 < 1, and some properties of that class. Chapter 2 is devoted to understanding the properties by introducing the notion of Linearity, Di erentiability, and majorants. A majorant function is a certain generalization of the power functions t , this is done in the rst section. In the second section we introducing the notion of moduli of continuity with its Some Properties which gotten from I.M. Kolodiy, F. Hildebrand paper [39]. In third section we produced harmonic mapping as preliminary for the fourth section which including subharmonicity of jfjq of harmonic quasiregular mapping in space. In the last section we introducing estimation of the Poisson kernel which were extracted from Krantz paper [42]. Chapter 3 is divided into 3 sections. This chapter is include the main result in this dissertation. In this chapter we prove that !u( ) C!f ( ), where u : ! Rn is the harmonic extension of a continuous map f : @ ! Rn, if u is a K-quasiregular map and is bounded in Rn with C2 boundary. Here C is a constant depending only on n, !f and K and !h denotes the modulus of continuity of h. We also prove a version of this result for !-extension domains with c-uniformly perfect boundary and quasiconformal mappings, and we state some results regarding HQC self maps of the quadrant Q = fz : z = x + iy; x; y > 0g. URI: http://hdl.handle.net/123456789/3048 Files in this item: 1
Ali Ababaoub Li ... asicionformal Mappings.pdf ( 501.4Kb ) -
Mišković, Vojislav (Belgrade , 1939)[more][less]
URI: http://hdl.handle.net/123456789/465 Files in this item: 1
VojislavMiskovi ... eLUniversiteDeBelgrade.pdf ( 2.547Mb ) -
Dautović, Šejla (Beograd , 2022)[more][less]
Abstract: The goal of this dissertation is to develop logics with the aim of formalizing Bayesian confirmation theory. As such, the very topic of this dissertation is in the field of probabilistic logic. In Bayesian theory there are qualitative and quantitative concepts of confirmation. Ac- cording to the first of these two terms, the event E probabilistically confirms the second event F if the conditional probability of the event F (with the condition E) is greater than unconditional probabilities. On the other hand, the quantitative approach studies the degree to which E confirms F , which is formalized by relevance measures of confirmation, binary functions with arguments E and F . Carnap used the notion of the degree of confirmation as the basic term for the formal apparatus of inductive logic. The main results of the dissertation are probabilistic logics with operators of confirma- tion that correspond to existing measures of relevance from the literature, and theoretical predictions related to these logics, such as deduction and completeness theorems, as well as decision results. The importance of the development of such logical systems, except in the direct formalization of important Bayesian concepts, lies in their expressiveness: for each measure of relevance that will be logically formalized, the resulting logical language is rich enough to express many basic operators of probabilistic logic from the literature, which are the operators of standard probability, qualitative confirmation and independence. The com- pleteness of these logical systems is proven in relation to the standard class of measurable models, which consist of Kripke’s structures in which the accessibility relation is replaced by a probabilistic measure defined over all possible worlds. The second part of the dissertation is about dynamic aspect of confirmation in the sense that we monitor how much the realization of an event affects the realization of another event in the future. Accordingly, in this dissertation we constructed a branching-time temporal logic with ac- tions and probabilistic confirmation operators. The results of the first part were successfully modified to obtain the completeness result of this logic URI: http://hdl.handle.net/123456789/5452 Files in this item: 1
Doktorska_disertacija_sdautovic.pdf ( 1.181Mb )