Browsing Mathematics by Title
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Rizvanolli, Fuat (Belgrade , 1982)[more][less]
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Kordić, Stevan (Beograd , 2016)[more][less]
Abstract: Constrain satisfaction problems including the optimisation problems are among the most important problems of discrete mathematics with wide area of application in mathematics itself and in the applied mathematics. Dissertation study optimisation problem and presents an original method for finding its exact solution. The name of the method is Sedimentation Algorithm, which is introduced together with two heuristics. It belongs to the class of branch-and-bound algorithms, which uses backtracking and forward checking techniques. The Sedimentation Algorithm is proven to be totally correct. Ability of the Sedimentation Algorithm to solve different type of problems is demonstrated in dissertation by its application on the Boolean satisfiability problems, the Whitehead Minimisation Problem and the Berth Allocation Problem in container port. The best results are obtained for Berth Allocation Problem, because its modelling for Sedimentation Algorithm includes all available optimisation techniques of the method. The precise complexity estimation of the Sedimentation Algorithm for the Berth Allocation Problem is established. Experimental results verify that the Sedimentation Algorithm is capable to solve the Berth Allocation Problem on the state of art level. URI: http://hdl.handle.net/123456789/4413 Files in this item: 1
StevanKordic.pdf ( 2.477Mb ) -
Kapetanović, Miodrag (Belgrade)[more][less]
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Ćelić, Momir (Banjaluka , 1986)[more][less]
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Marković, Zoran (Pennsylvania)[more][less]
Abstract: The results from this thesis are obtained by using notions and procedures which are well-known in Kripke structures in the first place, together with some other constructions. They might provides insights about intuitionistic formal theories analogous to insights about classical logic provided by results of classical model theory. The thesis consists of three chapters. The definitions concerning syntax of the first order intuitionistic logic, the definitions and theorems about Kripke structures, Hayting algebras and saturated theories are given in Chapter 1. In the first part of the next chapter a few results about the connection between forcing and classical satisfaction relation are proved. In the second part of that chapter three alternatives of the antecedent of the omitting type theorem are presented, and an omitting types theorem is proved. It is important that there are many applications of that theorem. In Chapter 3 the following two kinds of products are considered: prime products of saturated theories and ultra products and reduced products of Kripke structures. In the first part of that chapter the following property is proved: a simple analogue of ultraproduct construction can be defined in terms of saturated theories. The important result from the second part of Chapter 3 is that the class of formulas preserved under reduced products is much broader than the class of formulas which are intuitionistically equivalent to Horn formulas. URI: http://hdl.handle.net/123456789/317 Files in this item: 1
phdZoranMarkovic.pdf ( 9.114Mb ) -
Mihajlović, Borivoje (Belgrade , 1964)[more][less]
URI: http://hdl.handle.net/123456789/227 Files in this item: 1
phdBorivojeMihajlovic.pdf ( 2.509Mb ) -
Manojlović, Vesna (Beograd , 2008)[more][less]
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Marjanović, Miroslav (Belgrade)[more][less]
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Kamberi, Qerim (Priština)[more][less]
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Janković, Slobodan (Beograd , 1979)[more][less]
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Marković, Marijan (Belgrade , 2013)[more][less]
Abstract: This work consists of three chapters. The first one contains some well known facts about Hardy classes of harmonic, analytic, and logarithmically subharmonic functions in the unit disk, as well as their applications. Then we briefly talk about the harmonic and minimal surfaces, the classical isoperimetric inequality, and the more recent results related to this inequality. One of the most elegant way to establish the isoperimetric inequality is via Carleman’s inequality for analytic functions in disks. In the second chapter we present the results from our recent work [29] for harmonic mappings of a disc onto a Jordan surface. In this chapter we establish the versions of classical theorems of Carath´eodory and Smirnov for mappings of the previous type. At the end of the head we apply these results to prove the isoperimetric inequality for Jordan harmonic surfaces bounded by rectifiable curves. In the third chapter, according to the author paper [35], we prove an inequality of the isoperimetric type, similar to Carleman’s, for functions of several variables. The first version of this inequality is for analytic functions in a Reinhardt domain. The second one concerns the functions that belong to Hardy spaces in polydiscs. URI: http://hdl.handle.net/123456789/2586 Files in this item: 1
Markovic_Marijan.pdf ( 709.3Kb ) -
Lazarević, Milan (Beograd , 2020)[more][less]
Abstract: ist of already known and recently established Cauchy-Schwarz inequalities fore lementary operators,σ-elementary transformers and inner product type transformers iscomplemented by the next variant of Cauchy-Schwarz inequality in Schatten-von Neumann ideals: ZΩAtA∗tdμ(t) 12q−12ZΩAtXBtdμ(t) ZΩB∗tBtdμ(t) 12r−12p6 ZΩA∗tAtdμ(t) 12qX ZΩBtB∗tdμ(t) 12rpfor allX2Cp(H)and for allp, q, r>1which satisfies2p=1q+1r,if families of operatorsfAtgt∈Ω,fA∗tgt∈Ω,fBtgt∈Ω,fB∗tgt∈Ωare strongly square integrabile, such thatRΩAtA∗tdμ(t)andRΩB∗tBtdμ(t)are (boundedly) invertible operators.Enabled by some additional conditions of commutativity and normality for operator fami-liesfAng∞n=1,fBng∞n=1,fAtgt∈ΩandfBtgt∈Ω,as well as by the degree ofp-modifications ofunitary invariant norms, some others variants of those inequalities will also be considered,including their applications to the certain problems in operator theory, norm inequalities forgeneralized function derivations of Pick operator values functions and operator values Fouriertransformations of complex measures, as well as some Grüss-Landau type inequalities. URI: http://hdl.handle.net/123456789/5092 Files in this item: 1
disertacija_Lazarevic_Milan_dorada.pdf ( 1.868Mb ) -
Kovačević, Ilija (Belgrade)[more][less]
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Gilezan, Koriolan (Belgrade)[more][less]
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Jovanović, Boško (Belgrade)[more][less]
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Hoxha, Isak (Priština)[more][less]
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Mihajlović, Bojana (Beograd , 2016)[more][less]
Abstract: The subject of this dissertation belongs to scientific field of spectral graph theory, a young branch of mathematical combinatorics, i.e. graph theory, which finds important applications in many areas, such as chemistry, physics, computer science, telecommunications, sociology, etc., and various fields of mathematics. Spectral graph theory connects basic properties and the structure of a graph with characteristics of the spectra of its matrices (adjacency matrix, Laplacian matrix, etc.). In this dissertation we only work with the adjacency matrix. The second largest eigenvalue of the adjacency matrix of a graph (or, simply, second largest eigenvalue of a graph), as well as its distance from the largest eigenvalue, are very important especially in applications of spectral graph theory in computer science. The property of a graph that one of its eigenvalues does not exceed some given value is a hereditary one; therefore, many of the investigations of this kind have been directed at finding the maximal allowed graphs, or minimal forbidden graphs for that property. In this dissertation we determine some classes of graphs whose second largest eigenvalue does not exceed some given value, and, for that purpose, we develop some very useful tools. In methodological sense, investigations in this dissertation represent a combined approach consisting of application of the algebraic apparatus and methods of spectral graph theory and combinatorial reasoning, whilst at some stages the expert system newGRAPH has been used. The dissertation consists of eight chapters, each of which is divided into subchapters. In the beginning, some important previous work is shown, and afterwards we present some original elements of the algebraic and combinatorial apparatus that speed up and simplify the further work. We define some mappings between certain families of graphs, some of which preserve the sign of the expression 2 2 , and, using them, we describe and systematize some (already known) results in a new way. Further on we completely determine all maximal reflexive tricyclic cacti which are not RS-decidable and whose cycles do not form a bundle, from the classes 1 R and 3 R , and we give some partial results about the class 2 R , using previously induced mappings (until now only the graphs from the remaining class 4 R have been completely determined [40], [46]). Next, we completely describe all minimal forbidden graphs in the class of bicyclic graphs with a bridge, and all minimal forbidden graphs in the class 3 R - the approach that so far has never been used with reflexive graphs. Then we determine the maximal number of the cycles for RS-undecidable reflexive cacti whose cycles do form a bundle, and, therefore, generally for RS-undecidable reflexive cacti and we describe three classes of maximal reflexive RS-undecidable reflexive cacti that contain a bundle. Further on, some of the previous results are generalized: the generalized RS-theorem is stated and proved (so-called GRS-theorem) for any r , r 0 ; previously induced mappings are generalized, their properties are proved and various examples of classes of graphs with the property 2 r (for r 0 ) are given. Based on this, we describe all GRS-undecidable maximal graphs for the property 2 2 in the class of unicyclic and multicyclic graphs, and also all RS-undecidable maximal θ-graphs for this property as well as all GRS-undecidable maximal trees with the property 2 5 1 2 . Furthermore, we investigate the limit 3 (as in [28]) and we describe all trees with the diameter 3 and the diameter larger than 8, with the property 2 3 , as well as all GRSundecidable multicyclic cacti with the same property. Finally, we introduce and apply so-called σ-modifications of Smith trees. We describe seven σ-modifications and corresponding extensions, and we notice the appearance in (already known) results in the class of multicyclic reflexive cacti with 4 cycles. Applying some extensions to certain families of tricyclic cacti, we obtained the results in the class of multicyclic reflexive cacti with 4 cycles, using a different approach [48]. Finally, in the conclusion, we suggest some possible directions of further investigations. URI: http://hdl.handle.net/123456789/4445 Files in this item: 1
Mihailovic_Bojana.pdf ( 6.960Mb ) -
Acketa, Dragan (Novi Sad , 1984)[more][less]
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Vučemilović, Ante (Belgrade)[more][less]
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Cerović, Blagoje (Novi Sad , 1982)[more][less]