Browsing Doctoral Dissertations by Title

Knežević, Miljan (Beograd , 2014)[more][less]
Abstract: This thesis considers various properties of Euclidean harmonic mappings, quasiconformal mappings and generalized harmonic mappings, which are harmonic with respect to the conformal metric on the image surface. In particular, we obtained the answers to many questions concerning these classes of functions and that are related to the determination of different properties that are of essential importance for validity of the results such as those that generalize famous inequalities of the SchwarzPick type. The approach used was geometrical in nature, via analyzing the properties of the Gaussian curvature of the conformal metrics we are dealing with. URI: http://hdl.handle.net/123456789/4280 Files in this item: 1
phdKNEZEVIC_MILJAN.pdf ( 1.312Mb ) 
Vrećica, Siniša (Belgrade , 1984)[more][less]

Grujić, Vladimir (Belgrade)[more][less]

Alqifiary, Qusuay Hatim Eghaar (Beograd , 2015)[more][less]
Abstract: This thesis has been written under the supervision of my mentor Prof. dr. Julka Knezevi cMiljanovi c at the University of Belgrade in the academic year 20142015. The aim of this study is to investigate HyersUlam stability of some types of differential equations, and to study a generalized HyersUlam stability and as well as a special case of the HyersUlam stability problem, which is called the superstability. Therefore, when there is a differential equation, we answer the three main questions: 1 Does this equation have Hyers Ulam stability? 2 What are the conditions under which the differential equation has stability ? 3 What is a HyersUlam constant of the differential equation? The thesis is divided into three chapters. Chapter 1 is divided into 3 sections. In this chapter, we introduce some sufficient conditions under which each solution of the linear differential equation u′′(t) + ( 1 + (t) ) u(t) = 0 is bounded. Apart from this we prove the HyersUlam stability of it and the nonlinear differential equations of the form u′′(t) + F(t; u(t)) = 0, by using the Gronwall lemma and we prove the HyersUlam stability of the secondorder linear differential equations with boundary conditions. In addition to that we establish the superstability of linear differential equations of secondorder and higher order with continuous coefficients and with constant coefficients, respectively. Chapter 2 is divided into 2 sections. In this chapter, by using the Laplace transform method, we prove that the linear differential equation of the nthorder y(n)(t) + nΣ1 k=0 ky(k)(t) = f(t) has the generalized HyersUlam stability. And we prove also the HyersUlam Rassias stability of the secondorder linear differential equations with initial and boundary conditions, as well as linear differential equations of higher order in the form of y(n)(x) + (x)y(x) = 0, with initial conditions. Furthermore, we establish the generalized superstability of differential equations of nthorder with initial conditions and investigate the generalized superstability of differential equations of secondorder in the form of y′′(x)+p(x)y′(x)+q(x)y(x) = 0. Chapter 3 is divided into 2 sections. In this chapter, by applying the xed point alternative method, we give a necessary and sufficient condition in order that the rst order linear Alqi ary Abstract ii system of differential equations z_(t) + A(t)z(t) + B(t) = 0 has the HyersUlam Rassias stability and nd HyersUlam stability constant under those conditions. In addition to that, we apply this result to a secondorder differential equation y (t) + f(t)y_(t) + g(t)y(t) + h(t) = 0. Also, we apply it to differential equations with constant coefficient in the same sense of proofs. And we give a sufficient condition in order that the rst order nonlinear system of differential equations has HyersUlam stability and HyersUlamRassias stability. In addition, we present the relation between practical stability and HyersUlam stability and also Hyers UlamRassias stability. URI: http://hdl.handle.net/123456789/4295 Files in this item: 1
phdQusuayAlqifiary.pdf ( 259.8Kb ) 
Vukomanović, Đorđe (Belgrade , 1985)[more][less]
Abstract: The thesis consists of three chapters. In Chapter 1 nonstrict deductive implicative algebras are studied. Weak deductive, ndeductive and ωdeductive implicative algebras are introduced. Two kinds of complements, pseudocomplement and contraposition complement in deductive implicative algebras are defined, and the connection between these algebras and deductive implicative algebras with complement are presented. Certain properties of several implicative filters in implicative algebras and their connections with homomorphsms and congruences of these algebras are studied. In the last part of Chapter 1 the representation theorems for implicative algebras mentioned in the previous parts of the chapter are proved. The strict deductive implicative algebras and their properties, which are analogous to the properties algebras from the first chapter, are studied in Chapter 2. In the last part of that chapter the representation theorems for the strict implicative algebras are proved. In Chapter 3 deductive implicative algebras in the context of deductive (sub)nets are studied. Important notions of different forms of limited distribution and many interesting connections between these distributions and the properties of deductive nets are presented. It is shown that an implicative algebra can be drowned isomorphicaly into finite deductive subnet of sets or a net such that the implication are preserved. URI: http://hdl.handle.net/123456789/40 Files in this item: 1
phdDjordjeVukomanovic.pdf ( 6.744Mb ) 
Damljanović, Goran (Faculty of Mathematics, University of Belgrade , 2007)[more][less]

Vujošević, Biljana (Beograd , 2015)[more][less]
Abstract: In this doctoral dissertation we de ne the index of product systems of Hilbert B B modules over a unital C algebra B. In detail, we prove that the set of all uniformly continuous units on a product system over a C algebra B can be endowed with a structure of leftright Hilbert B B module after identifying similar units by the suitable equivalence relation and we use that construction to de ne the index of a given product system. We prove that such de ned index is a covariant functor from the category of continuous product systems to the category of twosided BB modules. We prove that the index is subadditive with respect to the outer tensor product of product systems and we, also, prove additional properties of the index of product system that can be embedded into a spatial one (a product system that contains a central unital unit). We prove that such de ned index is a generalization of earlier de ned indices by Arveson (in the case B = C) and Skeide (in the case of spatial product systems). We, also, de ne the index of product systems in a di erent way and prove that the new de nition is equivalent to the previous one. Actually, it corresponds to Arveson's original de nition of the index. URI: http://hdl.handle.net/123456789/4235 Files in this item: 1
phdBiljanaVujosevic.pdf ( 14.03Mb ) 
Mladenović, Miljana (Beograd , 2016)[more][less]
Abstract: The beginning of the new millennium was marked by huge development of social networks, internet technologies in the cloud and applications of artificial intelligence tools on the web. Extremely rapid growth in the number of articles on the Internet (blogs, ecommerce websites, forums, discussion groups, and systems for transmission of short messages, social networks and portals for publishing news) has increased the need for developing methods of rapid, comprehensive and accurate analysis of the text. Therefore, remarkable development of language technologies has enabled their applying in processes of document classification, document clustering, information retrieval, word sense disambiguation, text extraction, machine translation, computer speech recognition, natural language generation, sentiment analysis, etc. In computational linguistics, several different names for the area concerning processing of emotions in text are in use: sentiment classification, opinion mining, sentiment analysis, sentiment extraction. According to the nature and the methods used, sentiment analysis in text belongs to the field of computational linguistics that deals with the classification of text. In the process of analysing of emotions we generally speak of three kinds of text classification: • identification of subjectivity (opinion classification or subjectivity identification) used to divide texts into those that carry emotional content and those that only have factual content • sentiment classification (polarity identification) of texts that carry emotional content into those with positive and those with negative emotional content • determining the strength or intensity of emotional polarity (strength of orientation). In terms of the level at which the analysis of feelings is carried out, there are three methodologies: an analysis at the document level, at the sentence level and at the level of attributes. Standardized methods of text classification usually use machine learning methods or rulebased techniques. Sentiment analysis, as a specific type of classification of documents, also uses these methods. This doctoral thesis, whose main task is the analysis of emotions in text, presents research related to the sentiment classification of texts in Serbian language, using a probabilistic method of machine learning of multinomial logistic regression i.e. maximum entropy method. The aim of this research is to create the first comprehensive, flexible, modular system for sentiment analysis of Serbian language texts, with the help of digital resources such as: semantic networks, specialized lexicons and domain ontologies. This research is divided into two phases. The first phase is related to the development of methods and tools for detecting sentiment polarity of literal meaning of the text. In this part of the work, a new method of reducing the feature vector space for sentiment classification is proposed, implemented and evaluated. The proposed method for reduction is applied in the classification model of maximum entropy, and relies on the use of lexicalsemantic network WordNet and a specialized sentiment lexicon. The proposed method consists of two successive processes. The first process is related to the expansion of feature vector space by the inflectional forms of features. The study has shown that usage of stemming in sentiment analysis as a standard method of reducing feature vector space in text classification, can lead to incomplete or incorrect sentimentpolarity feature labelling, and with the introduction of inflectional feature forms, this problem can be avoided. The paper shows that a feature vector space, increased due to the introduction of inflectional forms, can be successfully reduced using the other proposed procedure – semantic mapping of all predictors with the same sentimentpolarity into a small number of semantic classes. In this way, the feature vector space is reduced compared to the initial one, and it also retains the semantic precision. The second phase of the dissertation describes the design and implementation of formal ontologies of Serbian language rhetorical figures – the domain ontology and the task ontology. Usage of the task ontology in generating features representing figurative speech is presented. The research aim of the second phase is to recognize figurative speech to be used in improving of the existing set of predictors generated in the first phase of the research. The research results in this phase show that some classes of figures of speech can be recognized automatically. In the course of working on this dissertation, a software tool SAFOS (Sentiment Analysis Framework for Serbian), as an integrated system for sentiment classification of text in Serbian language, has been developed, implemented and statistically evaluated. Results of the research within the scope of this thesis are shown in papers (Mladenović & Mitrović, 2013; Mladenović & Mitrović, 2014; Mladenović, Mitrović & Krstev, 2014; Mladenović, Mitrović, Krstev & Vitas, 2015; Mladenović, Mitrović & Krstev, 2016). The dissertation consists of seven chapters with the following structure. Chapter 1 introduces and defines methods, resources and concepts used in the first phase of research: text classification, sentiment classification, machine learning, supervised machine learning, probabilistic supervised machine learning, and language models. At the end of the introductory section, the tasks and objectives of the research have been defined. Chapter 2 presents a mathematical model of text classification methods and classification of sentiment methods. A mathematical model of a probabilistic classification and an application of the probabilistic classification in regression models are presented. At the end of the chapter it is shown that the method using the mathematical model of maximum entropy, as one of the regression models, has been successfully applied to natural language processing tasks. Chapter 3 presents the lexical resources of the Serbian language and the methods and tools of their processing. Chapter 4 deals with the comprehensive research on the currently available types and methods of sentiment classification. It shows the current work and research in sentiment classification of texts. It also presents a comparative overview of research in sentiment classification of texts using the method of maximum entropy. Chapter 5 discusses the contribution of this thesis to methods of feature space reduction for maximum entropy classification. First, a feature space reduction method is analysed. A new feature space reduction method which improves sentiment classification is proposed. А mathematical model containing proposed method is defined. Learning and testing sets and lexicalsemantic resources that are used in the proposed method are introduced. Chapter 5 also describes building and evaluation of a system for sentiment classification – SAFOS, which applies and evaluates the proposed method of a feature vector space reduction. The parameters and the functions of SAFOS are defined. Also, measures for evaluation of the system were discussed – precision, recall, F1measure and accuracy. A description of the method for assessing the statistical significance of a system is given. Also, implementation of the statistical test in the system SAFOS is discussed. The chapter provides an overview of the presented experiments, results and evaluation of the system. Chapter 6 deals with methods of recognizing figurative speech which can improve sentiment classification. The notion of domain ontology is introduced, the role of rhetorical figures and domain ontology of rhetorical figures. The importance of figurative speech in the sentiment classification has been explored. The description of the construction and structure of the first domain ontology of rhetorical figures in Serbian language, RetFig.owl, is given. Also, the description of the construction and structure of the corresponding task ontology that contains rules for identification of some classes of rhetorical figures is given. At the end of this chapter, an overview of the performed experiments, results and evaluation of the SAFOS system plugin that improved the recognition of figurative speech is given. The final chapter of this study deals with the achievemnts, problems and disadvantages of the SAFOS system. The conclusion of this thesis points to the great technological, social, educational and scientific importance of the sentiment analysis and recognition of the figurative speech and gives some routes in further development of the SAFOS system. URI: http://hdl.handle.net/123456789/4422 Files in this item: 1
Mladenovic_Miljana.pdf ( 13.60Mb ) 
Jovanović, Božidar (Beograd , 1999)[more][less]
URI: http://hdl.handle.net/123456789/4130 Files in this item: 1
Integrabilni_neholonomni.PDF ( 1.700Mb ) 
Shafah, Osama (Belgrade , 2013)[more][less]
Abstract: In this thesis we will give an interesting relation between finite rings and their graphs, such relations are obtained in following way. Consider a directed graph on a finite ring , where are sets of vertices and edges respectively, and defined by . Since is finite, it has an integer characteristic . If is not a prime, then has zero divisors and is not a unique factorization ring, but if it is prime, then nevertheless could have zerodivisors (e.g., ). Let and be relatively prime numbers, such that , ! and define two maps " #, $ by " %& and %& respectively, so " and are homomorphism maps, suppose that '() *+,. / + is a directed cycle of length . in a directed graph , then many interesting algebraic relations will exist between longest cycles in , # and $, which will be shown up in the chapter III. URI: http://hdl.handle.net/123456789/3052 Files in this item: 1
Doctroral_theiss_Osama_Shafah.pdf ( 332.8Kb ) 
Turku, Haljilj (Pristina , 1978)[more][less]

Pažanin, Ratomir (Belgrade , 1980)[more][less]

Stojanović, Milan (Beograd , 2017)[more][less]
Abstract: The goal of this dissertation is to determine values of local dynamical constants. This goal is achieved through examination of multiple samples of selected stars near the Sun. The selection is done by using planar and vertical eccentricities as sampling criteria. The solution for calculating eccentricities is given. In the next step a large sample of stars is selected by defining upper limits for eccentricities and vertical amplitude. Then nested subsamples are formed in two ways: in the first one upper eccentricity limit is subjected to decreasing, in the other one this is the case with upper amplitude of oscillations perpendicular to the plane. The values of the local dynamical constants are deduced by analysing this material. URI: http://hdl.handle.net/123456789/4498 Files in this item: 1
Stojanovic_Milan_teza.pdf ( 8.577Mb ) 
Sadžakov, Sofija (Belgrade)[more][less]

Mitrinović, Dragoslav (Beograd , 1933)[more][less]

Marovac, Ulfeta (Beograd , 2015)[more][less]
Abstract: Proteins are signi cant biological macromolecules of polymeric nature (polypeptides), which contain amino acids and are basic structural units of each cell. Their contents include 20+3 amino acids and, as a consequence, they are presented in biological databases as sequences formed from 23 di erent characters. Proteins can be classi ed based on their primary structure, secondary structure, function etc. One of possible classi cations of proteins by their function is related to their contents in a certain cluster of ortholologous groups (COGs). This classi cation is based on the previous comparison of proteins by their similarities in their primary structures, which is most often a result of homology, i.e. their mutual (evolutionary) origin. COG database is obtained by comparison of the known and predicted proteins encoded in the completely sequenced prokaryotic (archaea and bacteria) genomes and their classi cation by orthology. The proteins are classi ed in 25 categories which can be ordered in three basic functional groups (the proteins responsible for: (1) information storage and processing; (2) cellular processes and signaling; and (3) metabolism), or in a group of poorly characterized proteins. Classi cation of proteins by their contents in certain COG category (euKaryote Orthologous Groups KOG for eukaryotic organisms) is signi cant for better understanding of biological processes and various pathological conditions in people and other organisms. The dissertation proposed the model for classi cation of proteins in COG categories based on amino acid ngrams (sequences of n length). The set of data contains protein sequences of genomes from 8 di erent taxonomic classes [TKL97] of bacteria (Aqui cales, Bacteroidia, Chlamydiales, Chlorobia, Chloro exia, Cytophagia, Deinococci, Prochlorales), which are known to have been classi ed by COG categories. The new method is presented, based on the generalized systems of Boolean equations, used for separation of ngrams characteristic for proteins of corresponding COG categories. The presented method signi cantly reduces the number of processed ngrams in comparison to previously used methods of ngram analysis, iv thus more memory space is provided and less time for protein procession is necessary. The previously known methods for classi cation of proteins by functional categories compared each new protein (whose function had to be determined) to the set of all proteins which had already been classi ed by functions in order to determine the group which contained most similar proteins to the one which was to be classi ed. In relation to the previous, the advantage of the new method is in its avoidance of sequencesequence comparison and in search for those patterns (ngrams, up to 10 long) in a protein which are characteristic of the corresponding COG category. The selected patterns are added to a corresponding COG category and describe sequences of certain length, which have previously appeared in that COG category only, not in the proteins of other COG categories. On the basis of the proposed method, the predictor for determination of the corresponding COG category for a new protein is implemented. Minimal precision of the prediction is one of the predictors arguments. During the test phase the constructed predictor shown excellent results, with maximal precision of 99% reached for some proteins. According to its properties and relatively simple construction, the proposed method can be applied in similar domains where the solution of problem is based on ngram sequence analysis. URI: http://hdl.handle.net/123456789/4308 Files in this item: 1
phdUlfetaMarovac.pdf ( 7.954Mb ) 
Stalevski, T. Marko (Belgrade, Gent , 2012)[more][less]
URI: http://hdl.handle.net/123456789/2487 Files in this item: 1
Marko_Stalevski_doktorska_disertacija.pdf ( 6.024Mb ) 
Jaćimović, Milojica (Belgrade)[more][less]

Alimpić, Branka (Belgrade)[more][less]

Prešić, Marica (Belgrade)[more][less]