Browsing Doctoral Dissertations by Title
-
Vuković, Josif (Belgrade , 1984)[more][less]
-
Glišović, Nataša (Beograd , 2018)[more][less]
Abstract: In this doctoral dissertation the modelling process has been taken into consideration in the presence of uncertainty. Two types of problems were analyzed: one is the optimization of the benefit/costs tradeoff during the distribution of the projects and the other is the classification of data described by the attributes among which some are missing. The basic problems during the modelling of the decision making in the presence of uncertainty are the choice of the adequate treatment of uncertainty and the choice of the method for making a decision. One of the aims of the work is investigating the benefits of applying the metaheuristic algorithms on the considered optimization problems. The main measure for the evaluation of their performances is the value of objective function (for both problems: optimization of benefit/costs tradeoff during the project scheduling and clustering of incomplete data). Considering the project scheduling problem the level of satisfaction related to the problem constraints could also be taken into account. The other evaluation criteria of the applied metaheuristic methods is the time required for finding the solution. The influence of the parameters which control the algorithms of the metaheuristic methods is examined, as well as their appropriate values leading to the maximum performances of the implementation could be reached on the tested examples of the considered problems. As for the optimization problem of the profit/costs tradeoff, the uncertainty is modelled by applying the triangle fuzzy problems and then the metaheuristic methods, simulated annealing and genetic algorithm were applied for solving the obtained fuzzy optimization problem. The tested problems are formulated by the fuzzification method which was suggested by (Ribeiro et al. 1999). The represented experimental results for the set of fuzzy problems show the efficiency of the applied methods: simulated annealing and genetic algorithm. Genetic algorithm seems to produce slightly better solution than the simulated annealing. However, both methods out performed the existing form the literature for about 20%. The secund part of the work deals with the clustering data problem with the missing values of the attributes and making decisions in such circumstances. The main phases in solving the considered problem are finding the most appropriate distance, which will be used in the cases when the data are missing for some reasons and choosing the method for solving the clustering problem. As the theoretical and practical contribution, the metric, based on the logic principles, was proposed. By applying the probability, the theorem was proved defining the values of the weighting coefficients related to attributes that describe the objects for clustering. The proposed metric was implemented in the variable neighborhood search metaheuristic method as well as in some of its modifications. The implemented methods have been applied on the real life problems from the literature. Classifying the patients who suffer from some auto-immune diseases, stored in the database of Clinical Centre of Serbia, the precision of the clustering of 93.33% was achieved. As another real life example, seven databases of the European Commision (Board), which contain the data for the mail service, have been analyzed. The clustering efficiency of 90% - 96.96% was achieved. In order to compare the efficiency of the approach based on the variable neighborhood search method, nine databases available on the internet were used and the obtained results were compared with the existing ones from the literature. The experiments showed large stability of variable neighborhood search method: in eight out of nine cases the best solution was reached in all hundred repetitions. Besides that, the quality of the obtained solutons have considerably surpassed the results from the literature. URI: http://hdl.handle.net/123456789/4710 Files in this item: 1
Nglis_DoktorskaDisertacija.pdf ( 3.362Mb ) -
Jovović, Ivana (Belgrade , 2013)[more][less]
Abstract: This dissertation deals with an application of some linear algebra techniques for solving problems of reduction of system of linear operator equation of the form A(x1) = b11x1 + b12x2 + : : : + b1nxn + '1 A(x2) = b21x1 + b22x2 + : : : + b2nxn + '2 ... A(xn) = bn1x1 + bn2x2 + : : : + bnnxn + 'n; where B = [bij ]n n is matrix over the eld K, A is linear operator on the vector space V over K and where '1; '2; : : : ; 'n are vectors in V . In particular, we consider reduction of such system under the action of the general linear group GL(n;K) and also reduction by using the characteristic polynomial B( ) of the matrix B and recurrence for the coe cients of the adjugate matrix of the characteristic matrix I B of the matrix B. The idea is to use rational and Jordan canonical forms to reduce the linear system of operator equations to an equivalent partially reduced system, i.e. to decompose the initial system into several uncoupled systems. This represents a new application of doubly companion matrix introduced by J.C. Butcher in [5]. In this work we are also concerned with transformation of the linear system of operator equation into totally reduced system, i. e. completely decoupled system of higher order linear operator equations. This results are related to results given by T. Downs in [13]. The thesis consists of two parts. The rst part deals with properties of rational and Jordan canonical form. We start with Fundamental Theorem of Finitely Generated Modules Over a Principle Ideal Domain. If we consider nite dimensional vector space V over K as module over the ring K[x] of polynomials in x with coe cients in K, the Fundamental Theorem implies that there is a basis for V so that the associated matrix for B is in rational or Jordan form. The rst section is adapted from Abstract Algebra of D. S. Dummit i R. M. Foote [14]. In the second section we look more closely at Hermite, Smith, rational and Jordan form and establish the relation between them. The structure of the similarity transformation matrix is also described. Some of theorem are considered from several aspects. This section provides a detailed exposition of normal forms using [14, 19, 37, 34, 35, 20, 57] and [1, 22, 48, 52, 54, 60]. The second part concerns with author's original contribution and it relies on papers [42, 43]. First we illustrate methods of the partial and the total reduction of systems v in two or three unknowns and then we study reductions of systems in n unknowns. The partial reduction requests changing of basis so that the system matrix is in the rational or Jordan form. We also treat the total reduction of the obtained partially reduced systems in this manner. Subsection 4.4. "Total Reduction for Linear Systems of Operator Equations with System Matrix in Companion Form" is one interesting way to proceed consideration started in previously mentioned works. It is based on papers of L. Brand [3, 4]. The fth section is generalization of the forth. Here we examine systems in n unknowns and with di erent linear operators. We introduce the notion of characteristic polynomial in more than one unknown - generalized characteristic polynomial and a method for total reduction by nding adjugate matrix of the generalized characteristic matrix of the system matrix. The sixth section is a summary of applications and examples of methods for partial and total reduction. There are some examples of the rst and higher order linear systems of di erential equations and di erent approaches for calculating rational and Jordan canonical forms. The last section is devoted to the study of di erential transcendence of the solution of the rst order linear system of di erential equations with complex coe cients, where exactly one of the following meromorphic functions '1; '2; : : : ; 'n is di erentially transcendental, using method of total reduction. We review some of the standard facts on di erential transcendence following books [45, 44, 39, 50, 7, 33, 15, 23, 36]. URI: http://hdl.handle.net/123456789/2585 Files in this item: 1
Jovović_Ivana.pdf ( 2.063Mb ) -
Ćirić, Ninoslav (Belgrade)[more][less]
-
Manojlović, V. Jelena (Belgrade , 1999)[more][less]
URI: http://hdl.handle.net/123456789/2491 Files in this item: 1
Manojlovic_Jelena_DR teza.pdf ( 829.5Kb ) -
Wotulo, Max (Belgrade)[more][less]
-
Stankov, Dragan (Belgrade , 2008)[more][less]
-
Janc, Mirko (Belgrade , 1981)[more][less]
-
Malešević, Branko (Belgrade)[more][less]
-
Tankosić, Milorad (Belgrade , 1984)[more][less]
-
Pejović, Aleksandar (University of Novi Sad, Faculty of Technical Sciences , 2020)[more][less]
Abstract: This dissertation is about the development of a parallel software system for representing and solving problems of finite model theory and its application. The theoretical foundation of the system is presented, as well as an in-depth explanation of the implementation in Python. In particular, a parallel method for computing Boolean expressions based on the properties of finite free Boolean algebras is developed. It is also shown how various finite combinatorial objects can be coded in the formalism of Boolean algebras and counted by this procedure. Specifically, using a translation of first order predicate formulas to propositional formulas, we developed a technique for constructing and counting finite models of first order theories. Finally, we have developed some general techniques that enable more effective use of our system. We illustrate these techniques on two examples. The first one deals with partial orders, while the other one is about random graphs. URI: http://hdl.handle.net/123456789/4857 Files in this item: 3
APejovicDissertation.pdf ( 1.253Mb )APejovicPhDPresentation.pdf ( 1.103Mb )APejovicPhDSoftwareSources.zip ( 25.25Kb ) -
Mikičić, Dušan (Belgrade , 1976)[more][less]
-
Kuzeljević, Boriša (Novi Sad , 2013)[more][less]
Abstract: The purpose of this thesis is to investigate chains in partial orders (P(X), C), where 11} (X) is the set of domains of isomorphic substructures of a relational structure X. Since each chain in a partial order can be extended to a maximal one, it is enough to describe maximal chains in P(X). It is proved that, if X is an ultrahomogeneous relational structure with non-trivial isomorphic substructures, then each maximal chain in (P(X) U {0} , C) is a complete, R-embeddable linear order with minimum non-isolated. If X is a relational structure, a condition is given for X, which is sufficient for (P(X) U {0} , C) to embed each complete, R-embeddable linear order with minimum non-isolated as a maximal chain. It is also proved that if X is one of the following relational structures: Rado graph, Henson graph, random poset, ultrahomogeneous poset 1,13, or ultrahomogeneous poset C, 2 ; then L is isomorphic to a maximal chain in (P(X) U {0} , C) if and only if L is complete, R-embeddable with minimum non-isolated. If X is a countable antichain or disjoint union of u complete graphs on v vertices with pv = then L is isomorphic to a maximal chain in 0P(X) U {0} , c) if and only if L is Boolean, R-embeddable with minimum non-isolated. URI: http://hdl.handle.net/123456789/3873 Files in this item: 1
PhD_Borisa_Kuzeljevic.PDF ( 937.1Kb ) -
Vasić, Velimir (Belgrade)[more][less]
-
Berisha, Fevzi (Priština)[more][less]
-
Komljenović, Stevo (Belgrade , 1964)[more][less]
-
Perić, Milan (Beograd , 2021)[more][less]
Abstract: his thesis presents a method for calculating the polynomial entropy of the topolog-ical dynamic system with finitely many non-wandering points. A special coding is adapted forsuch systems. Thanks to this coding the polynomial entropy can be bounded by the numberof specific mutually singular points in the closures of stable manifolds of non-wandering points.This method was applied to Morse gradient systems. It is shown that the polynomial entropyof the Morse gradient system is bounded byn(F) URI: http://hdl.handle.net/123456789/5215 Files in this item: 1
Milan_Peric_disertacija.pdf ( 731.8Kb ) -
Ivković, Stefan (Beograd , 2021)[more][less]
Abstract: In the first part of the thesis, we establish the semi-Fredholm theory on Hilbert C∗- modules as a continuation of the Fredholm theory on Hilbert C∗-modules which was introduced by Mishchenko and Fomenko. Starting from their definition of C∗-Fredholm operator, we give definition of semi-C∗-Fredholm operator and prove that these operators correspond to one-sided invertible elements in the Calkin algebra. Also, we give definition of semi-C∗-Weyl operators and semi-C∗-B-Fredholm operators and obtain in this connection several results generalizing the counterparts from the classical semi-Fredholm theory on Hilbert spaces. Finally, we consider closed range operators on Hilbert C∗-modules and give necessary and sufficient conditions for a composition of two closed range C∗-operators to have closed image. The second part of the thesis is devoted to the generalized spectral theory of operators on Hilbert C∗-modules. We introduce generalized spectra in C∗-algebras of C∗-operators and give description of such spectra of shift operators, unitary, self-adjoint and normal operators on the standard Hilbert C∗- module. Then we proceed further by studying generalized Fredholm spectra (in C∗-algebras) of operators on Hilbert C∗-modules induced by various subclasses of semi-C∗-Fredholm operators. In this setting we obtain generalizations of some of the results from the classical spectral semi-Fredholm theory such as the results by Zemanek regarding the relationship between the spectra of an operator and the spectra of its compressions. Also, we study 2×2 upper triangular operator matrices acting on the direct sum of two standard Hilbert C∗-modules and describe the relationship between semi-C∗-Fredholmness of these matrices and of their diagonal entries. URI: http://hdl.handle.net/123456789/5305 Files in this item: 1
Stefan_Ivkovic_Doktorska_disertacija.pdf ( 1.505Mb ) -
Živanović, Žarko (Belgrade , 1974)[more][less]
-
Ćirić, Ljubomir (Belgrade)[more][less]