Browsing Doctoral Dissertations by Title

Arsenović, Mihajlo (Belgrade)[more][less]

Pevac, Lazar (Belgrade)[more][less]

Zeada, Samira (Belgrade , 2015)[more][less]

Zeada, Samira (Beograd , 2015)[more][less]

Ziada, Samira (Beograd , 2015)[more][less]
Abstract: This thesis has been written under the supervision of my mentor Prof. Aleksandar T. Lipkovski at the University of Belgrade in the academic year 2014 2015. The topic of this thesis is Classi cation of Monomial Orders In Polynomial Rings and Gr obner Basis. The thesis is divided into four chapters let us review the content and the main contributions to this doctoral thesis. In the rst chapter (page. 16), the de nitions, features and examples of the notions basic for this thesis are given. Also, relevant properties of the multivariate polynomial ring and the division with reminder algorithm are recalled. In Chapter 2 (page. 722), the classi cation of monomial orderings for multivariate polynomial rings is displayed (given) in detail, with special emphasis on the case of two variables. The connection of this classi cation and the well known classi cation of Robiano is exposed in detail. It is an unusual and a littleknown fact that the set of di erent monomial orderings with the natural topology is a Cantor set. Chapter 3 (page. 2340) and Chapter 4 (page. 4151) contain the main contributions of the thesis. In Chapter 3, the new approach to the analysis of the division with reminder algorithm is presented, based on set theoretic partial orderings (Section 3.3). Thus, the new evidence for (proof of ) Buchbergers result on niteness of the division procedure, regardless of a choice of the leading terms for the next dividing, is obtained. Likewise, in order to investigate Hilbert's original contribution and links with later considerations, we present his proof of the famous Hilbert basis theorem, on the basis of his original papers (section 3.5). In Chapter 4 (page. 4151), a result from Chapter 3 is used for another new characterization of Gr obner basis, apparently weaker than wellknown ones, to be obtained. Namely, it is shown that the bases G = ff1; : : : ; fkg of an ideal I is Gr obner if and only if, for any f from I, the support SuppG(f) is not empty. This condition is (only outwardly) weaker than a typical condition that the leading term of f belongs to SuppG(f). And describe the Gr obner fan of an ideal I and give an algorithm In a special case of two variables. URI: http://hdl.handle.net/123456789/4304 Files in this item: 1
phdSamiraZiada.pdf ( 465.6Kb ) 
Danić, Dimitrije (, 1885)[more][less]
Abstract: Tema Danićeve disertacije su konformna preslikavanja eliptičkog paraboloida na ravan, prateći definicije i formalizam koje je uveo Gaus (F. Gauss) za tu vrstu preslikavanja. U tom razmatranju izveo je određene parcijalne diferencijalne jednačine koje takođe analizira i rešava. Njegov doprinos bile su metode u rešavanju kompleksnih eliptičkih integrala, uvođenju eliptičkih transformacija i primeni eliptičkih funkcija u rešavanju ovih parcijalnih jednačina. URI: http://hdl.handle.net/123456789/4796 Files in this item: 3
DDanic_thesis_documentation.pdf ( 239.6Kb )DDanic_thesis_transl_SRB.pdf ( 1.764Mb )DDanic_thesis.pdf ( 1.420Mb ) 
Mijajlović, Žarko (Belgrade , 1977)[more][less]
Abstract: Part1. Basic notions of model theory are given. Part2. Dual notions in categories of Boolean algebras and Stone spaces are studied in respect to natural contravariant functor. The cellularity number of a Boolean algebra B, celB is studied, certain cardinal properties are proved, e.g. it is consistent with ZFC that celB is attained for every Boolean algebra B. Part3. Lindenbaum algebras of firstorder theories are studied in details. It is proved that every Boolean algebra is isomorphic to the Lindenbaum algebra B1 of Σ1 formulas of certain firstorder complete theory. Stability number ST(k) of a firstorder theory T is studied, and it is shown that ST(k) = Ku(k), where Ku(k) is the Kurepa number (Kurepa introduced it in 1935) and T is the theory of dense linear ordering without endpoints, while the cardinality of the Stone space of B1(A), A is a model of T, is equal to ded(A), the Dedekind number of the ordering A. Ku(k)= sup{ded(A): A is a model of T, A=k}. Part4. Σn Πn ramifications of various notions in model theory are defined and studied, e.g. elementary embeddings, completeness, chains, direct limits, diagram properties, etc. Preservation theorems for these types of formulas are proved. Examples for including ordered structures and algebraic fields are given. Part5. Model completions and elimination of quantifiers are studied. As an application, it is proved that by means of model theory that the classes of Boolean algebras and distributive lattices with the least and the greatest elements are Jonsson’s classes. Algebraic description of saturated models of submodelcomplete theories are given, unifying results of Haussdorff (dense linear ordering), Erdös, Gillman (ordered fields) and Boolean algebras (Negrepontis) for homogeneousuniversal models. Part6. Here is studied what modeltheoretic properties are absolute in ZF in the sense introduced by Levy, i.e. in which cases strong hypothesis (AC, GCH, V=L) can be eliminated from the proof of these properties. It is shown that the following properties of firstorder theories are absolute: the consistency, completeness, modelcompleteness and elimination of quantifiers. These gives new light on modeltheoretic proofs of these properties. URI: http://hdl.handle.net/123456789/196 Files in this item: 1
phdZarkoMijajlovic.pdf ( 27.39Mb ) 
Božić, Milan (Belgrade , 1983)[more][less]
Abstract: The thesis consists of five chapters. In the introductory chapter some relationaloperational structures building of sets of formulas in calculi RA^+ and R^+ are presented. These structures are used in other chapters in making of the canonical frames of Kripke’ type for semantic of positive fragments of relevant propositional calculi. In Chapter 1, the semantic of these positive fragments, which is a mixture of known Routley & Meyer’s and Maksimova’s semantics, is presented. A new way for the semantic of negation in relevant logics is introduced in Chapter 2. It this way semantic completeness theorems for a large class of expansions of the logic R_min are proved. It is shown that Routley & Meyer’s semantic for the logic R is a special case of that semantic. Relevant modal logics are studied in Chapter 3. A semantic of Kripke’s type by which a completeness of a large class of modal logics whose basics are different relevant calculi with or without negation is introduced. A characterization of a large class modal i.e. Hintikka, schemas is given too. They contain almost all modal schemas characterized by formulas of the first order. Moreover, it is proved that the only known semantic for the calculus R_⊙ is a special case of the semantic given in this chapter. Semantics of relevant calculi which are not distributive are studied in Chapter 4. It is shown that semantics of nondistributive relevant logics radically change Kripke’s semantic. URI: http://hdl.handle.net/123456789/340 Files in this item: 1
phdMilanBozic.pdf ( 36.24Mb ) 
Tošić, Ratko (Belgrade , 1978)[more][less]
Abstract: The thesis consists of five chapters. In Chapter 1 definitions and wellknown results from the theory of Boolean algebras and Boolean functions are given. In Chapter 2 of the thesis some properties of Boolean functions, which preserve constants under finite Boolean algebras, are presented by using the component representation. Their consequences about the number of Boolean’s functions are also given. The theorems which are the generalization of Scognmaiglio’s theorem and Andreoli’s theorem for Boolean functions with one variable, are proved in Chapter 3. The following new notions are introduced for monotone logical functions: the profile, the level, homogeneous, the corresponding matrix, etc. Some properties of these functions are shown and some consequences about the number of homogeneous monotone logical functions are presented. In Chapter 4 the applications of monotone Boolean functions in solving the problems of search theory (a branch of the theory of information) are presented. It is shown that the general problem of a type is, in fact, the problem of identifications of homogeneous monotone Boolean functions of the given profile by checking the value of that function for combinations of values of variables. Optimal or almost optimal solutions for some profiles are shown. It is also shown that monotonic logical functions are natural instrument for the generalization of these problems. Some open problems are presented in Chapter 5. URI: http://hdl.handle.net/123456789/356 Files in this item: 1
phdRatkoTosic.pdf ( 3.843Mb ) 
Vujošević, Slobodan (Belgrade , 1981)[more][less]
Abstract: The thesis consists of three chapters. Heyting algebras are studied as an equality category in Chapter 1. The properties of filters and ideals of Heyting algebras are presented together with corresponding properties in distributive nets and Boolean algebras. Free, injective and projective Heyting algebras are presented and a theorem about the representation in algebras with closing is proved. Some properties of Heyting algebras, which are important for study of formal logics closely to intuitionistic logic, are also presented. Complete Heyting algebras are studied in Chapter 2. The family of complete Heyting algebras is obtained by repeating of the construction of the algebra of Joperators. Some properties of this family when the initial Heyting algebras is linear order, are studied. Moreover, the characterization of complete Heyting algebras which can be approximated by complete Boolean algebras is given. Duality of categories of topological spaces and complete Heyting algebras are studied in Chapter 3. Some adjunctions are defined, and for those adjunctions the actions of monad and comonad are studied. It is shown that the category of complete Heyting algebras is reflective in the categories of sets, distributive bounded nets and complete Heyting algebras. It is shown that complete Heyting algebras correspond to "deposited" spaces, and distributive bounded nets correspond to a restriction of Ston’s spaces. URI: http://hdl.handle.net/123456789/89 Files in this item: 1
phdSlobodanVujosevic.pdf ( 3.553Mb ) 
Boričić, Branislav (Belgrade , 1983)[more][less]
Abstract: The thesis consists of four chapters. Chapter 1 contains a general framework for deductive systems and contains a sequenceconclusion natural deduction system for classical first order logic. A sequence NLC_n of intermediate propositional logics is considered in Chapter 2. It is shown that the sequence NLC_n contains three different systems only. These are the classical calculus NLC_1, Dummett's system NLC_2 and the logic NLC_3, an extension of the Heyting propositional logic by the axiom (A⇒B)∨(B⇒C)∨(C⇒A) . It is also shown that the logic NLC_3 is separable. In the sequel, the completeness of NLC_3 with respect to the corresponding Kripke type models having the property that ∀x∀y∀z(xRy∨yRz∨zRx) is proved, as well as its decidability and the independence of logical connectives. It is shown that some subsystems of NLC_3 are separable and that the limits of the considered systems is the Heyting propositional calculus. The logic of the weak law of excluded middle, an extension of the Heyting logic by ¬A∨¬¬A, is considered in Chapter 3. An embedding of classical logic into this logic is described and it is proved that this logic is the minimal one having this property. A Hilberttype formulation of implication fragment of the Heyting propositional logic formalizing the deducibility relation, is presented in Chapter 4, enabling to define a decision procedure based on a kind of cutelimination theorem. URI: http://hdl.handle.net/123456789/257 Files in this item: 1
phdBranislavBoricic.PDF ( 5.899Mb ) 
Antić, Miroslava (Belgrade)[more][less]

Alshafah, Samira (Beograd , 2018)[more][less]
Abstract: Proteins with intrinsically disordered regions are involved in large number of key cell processes including signaling, transcription, and chromatin remodeling functions . On the other side, such proteins have been observed in people suffering from neurological and cardiovascular diseases, as well as various malignancies. Process of experimentally determining disordered regions in proteins is a very expensive and long  term process. As a consequence, a various computer programs for predicting position of disordered regions in proteins have been developed and constantly improved. In this thesis a new method for determining Amino acid sequences that characterize ordered/disordered regions is presented. Material used in research includes 4076 viruses wit h more than 190000 proteins. Proposed method is based on defining correspondence between n grams (including both repeats and palindromic sequence s) characteristics and their belonging to ordered/disordered protein regions. Positions of ordered/disordered regions are predicted using three different predictors. The features of the repetitive strings used in the research include mol e fractions, fract ional differences, and z values. Also, data mining techniques association rules and classification were applied on both repeats and palindromes. The results obtained by all techniques show a high level of agreement for a short length of less than 6, while the level of agreement grows up to the maximum with increasing the length of the sequences. The high reliability of the results obtained by the data mining techniques shows that there are n grams, both repeating sequences and palindromes, which uniquely ch aracterize the disordered/ ordered regions of the proteins . The obtained results were verified by comparing with the results based on n grams from the DisProt database which contain s the positions of experimentally verified disordered regions of the protein. Results can be used both for the fast localization of disordered/ordered regions in proteins as well as for further improving existing programs for their prediction. URI: http://hdl.handle.net/123456789/4746 Files in this item: 1
ThesisSamira_Alshafah.pdf ( 3.106Mb ) 
Ćirić, Miroslav (Beograd , 1991)[more][less]

Ranković, Slavko (Belgrade , 1972)[more][less]

Živaljević, Rade (Belgrade , 1983)[more][less]

Elfaghine, Halima (Beograd , 2016)[more][less]
Abstract: The subject of this thesis belongs the area of quality control, which represents the practical usage of statistics in following and improving the production process. In 1930 Walter Shewhart started studying quality control, based on control charts, and using statistical principles. Later on, after World War II, Edward Deming took this discipline to Japan, where it ourished. The design and the performance of control charts are the most important problems in this area. The purpose of studying the characteristics of control charts in this thesis is to compare the existing and the suggested control charts. The thesis is divided into four chapters. The rst chapter is introductory and contains motivation and basic de nitions related to this subject. In this study it is always assumed that the data are normally distributed, and that the incontrol process data are stationary and uncorrelated. Shewhart control charts and the corresponding limits are constructed in order to meet the given speci cations for the quality characteristic that we investigate. Quality control that is applied to a production process always has costs related to the control. The important parameters connected to the cost of quality control are: width of control limits k, the sample size n and the interval between the samples h. In Chapter 2 a new loss function is given, which is connected to the production process and to X−bar quality control chart. Using Matlab program for optimization, values of ^k; ^n and ^h are found, which minimize the loss function for given costs. For given values of cost, a nonlinear regression model is built using a package Sigma plot and the obtained values are compared to those obtained by numerical optimization. In Chapter 3, the time series model Yi = Xi + (1 − )Yi−1 is investigated, where 0 < B 1 is a constant, Xi are N( ; 2) distributed. Exponentially Weighted Moving Average (EWMA) control charts for this model are presented, and type I and type II errors are calculated in the case when i is large. For di erent sample sizes, the new comparison between the optimal design of the Xbar and EWMA control charts for Normally distributed quality characteristic is given, comparing the corresponding costloss functions, power functions and average run lengths. i The process of calibration is one of the methods in statistical process control, introduced for improving the quality of the products and for reducing the production costs. In Chapter 4, two new models of nonsymmetrical loss function are introduced. Here, the loss function is connected to one product under control (not to the whole sample). Using our program, written in statistical software R, the value which minimizes the expected loss for Shewhart X control chart is found. This value is used as the new central target value of the quality characteristic, that is, the production process is calibrated with this new value. The thesis ends with Conclusions, where the results of the thesis are summarized, and with some open problems to be investigated. URI: http://hdl.handle.net/123456789/4340 Files in this item: 1
Disertacija_Halima_Elfaghihe.pdf ( 1.104Mb ) 
Vukićević, Petar (Berlin , 1894)[more][less]

Nešović, Emilija (Kragujevac, Serbia , 2011)[more][less]
Abstract: The field of research in this dissertation is consideration of different types of curves in Minkowski spaces, as well as defining the notion of hyperbolic angle between spacelike and timelike vector. The research in this dissertation is connected with the following subjects: geometry of hyperquadrics in Minkowski space, finite type submanifolds and plane Minkowski geometry. This dissertation, beside Preface and References with 56 items, consists of four chapters: 1. Curves in hyperquadrics in Minkowski spaces; 2. Classification of 2 –type curves in Minkowski nspace ; 3. Wcurves in Minkowski spacetime; 4. Hyperbolic angle between vectors. In Chapter 1 the curves lying in hyperquadrics in Minkovski 3space and Minkowski 4space are studied. More precisely, the results related with the spacelike and timelike curves lying pseudosphere in Minkowski 3space are presented. Also, the necessary and sufficient conditions for spacelike curves lying in pseudohyperbolic space in Minkowski 4space are given. Curves of finite type 2 in Minkowski nspace are studied in details in Chapter 2. Also, there are given some known results related with finite type submanifolds. In Chapter 3, Wcurves (i.e. the curves having constant all curvature functions) in Minkowski spacetime are studied and some relations between Wcurves and finite type curves are given. Finally, in Chapter 4 one of the basic notions in Lorentzian geometry is considered, i.e. hyperbolic angle between two nonnull vectors. The notion of hyperbolic angle between two timelike vectors is wellknown, so in this chapter it is defined the notion between spacelike and timelike vectors. The measure of hyperbolic angle is also defined. By using the notion of hyperbolic angle between spacelike and timelike vectors, all spacelike curves of constant precession with nonnull principal normal and all timelike curves of constant precession in Minkowski 3space are classified and their explicit parameter equations are given. URI: http://hdl.handle.net/123456789/1916 Files in this item: 1
Dokt. disertacija dr E. NešovićR.pdf ( 3.472Mb ) 
Pantić, Živadin (Belgrade)[more][less]