Browsing Doctoral Dissertations by Title

Albijanić, Miloljub (Matematički fakultet , 2016)[more][less]
Abstract: Osnovni koncept rada jeste povezanost apstraktne teorije i primenjene matematiˇcke analize u univerzalnom matematiˇckom sistemu. Matematika je doˇzivela veliku praktiˇcnu primenu, na primer, primenu matematiˇcke statistike, numeriˇcke analize, primene u elektrotehnici, doprinos razvoju raˇcunarstva i dr. Istovremeno, u nauˇcnom pogledu, uzdigla se do neslu´cenih apstrakcija (topoloˇski prostori, vektorski prostori i drugo). Zbog ovih ˇcinjenica neophodno je unapredivati nastavu matematiˇcke analize na tehniˇckim fakultetima ali i same metode nastave. Rad sadrˇzi teorijsko i empirijsko istraˇzivanje. Teorijsko istraˇzivanje rasvetljava pojmove apstrakcije i primene i daje primere iz slede´cih nastavnih tema: Lagranˇzova teorema, konveksnost i posledice; Tejlorova formula; Hardijev pristup za izraˇcunavanje povrˇsine ravne figure; Furijeovi redovi i primene; Banahova teorema o fiksnoj taˇcki i primene. Empirijsko istraˇzivanje sastoji se iz dva dela: upitnika i testa. Ovo istraˇzivanje otkriva kako odnos teorije i primene doˇzivljavaju studenti, kako vide nastavu matematike i koja nastavna sredstva koriste. Istraˇzivanje otkriva i kako studenti reˇsavaju jednostavne probleme i koju vrstu zadataka uspeˇsnije reˇsavaju. Uzorak ˇcini 429 studenata elektrotehnike, gradevine i maˇsinstva za Upitnik i 450 studenata istih fakulteta za Test. Studenti koji su uˇcestvovali u istraˇzivanju pohadaju Univerzitet u Beogradu, Univerzitet u Novom Sadu i Univerzitet u Niˇsu. Rezultati istraˇzivanja su potvrdili da studenti tehniˇckih fakulteta imaju pozitivan odnos prema matematici i da njen znaˇcaj vide kroz primenu, odnosno njenu upotrebnu vrednost. Studenti imaju jasno definisane stavove o tome da je dobro predavanje nastavnika ono koje je razumljivo, razgovetno i koje motiviˇse studente da u njemu uˇcestvuju. Istiˇcu znaˇcaj primera koji imaju elemente primene. Vizuelna prezentacija pove´cava uspeˇsnost reˇsavanja zadataka. Istraˇzivanje pokazuje da studenti nisu stekli veˇstinu da znanje iz matematiˇcke analize primene u reˇsavanju zadataka i problema. Teorijskim rasvetljavanjem pojmova apstrakcije i primene, a zatim prikazom pet tema matemati ˇcke analize, potvrdeno je da su apstraktna teorija i primenjena matematiˇcka analiza medusobno povezane i objedinjene u univerzalnom matematiˇckom sistemu. Na osnovu nalaza formulisane su preporuke koje se odnose na inovativne pristupe u nastavi kao ˇsto su planiranje nastave i unapredivanje sadrˇzaja, postavljanje pitanja, inteligentni pogled, poboljˇsanje predavanja i koriˇs´cenje nastavnih sredstava. Na ovaj naˇcin potvrduje se da metodiˇcki dobro postavljena nastava pomaˇze boljem razumevanju odnosa izmedu apstrakcije i primene matematiˇcke analize. Kljuˇcne reˇci: Matematiˇcka analiza, nastava, apstrakcija, primena, Lagranˇzova teorema, konveksnost, Furijeovi redovi, fiksna taˇcka. URI: http://hdl.handle.net/123456789/4684 Files in this item: 1
doktorat_albijanic.pdf ( 4.985Mb ) 
Albijanić, Miroljub (Beograd , 2016)[more][less]
Abstract: The main concept of this thesis is the connection of abstract theory and applied mathematical analysis in the universal mathematical system. The Mathematics is being applied practically in great number of cases, for example, in the application of mathematical statistics, numerical analysis, application in electrical engineering, contribution to computer developing etc. At the same time, in scientific perspective, it reached the level of incredible abstractions (topological spaces, vector spaces et al.). Due to these facts, it has become necessary to advance the teaching of mathematical analysis in technological universities, but also the very methods of teaching as well. This thesis contains both a theoretical and an empirical research. The theoretical research sheds light onto the notions of abstraction and application and gives examples from next teaching subjects: Lagrange’s Theorem, Convexity and Consequences. Taylor’s Formula. Hardy’s Approach to Calculating Surfaces of Flat Shapes. Fourier’s Series and their Application. Banach FixedPoint Theorem and its’ Application. The empirical research consists of two parts: a questionnaire and a test. This research shows how the relation between theory and application is seen by students, how they perceive the teaching of mathematics and which learning instruments they use. The research also shows how students solve simple problems and which type of problems they solve more sucessfully. The sample consists of 429 students of electrical engineering, construction and mechanical engineering for the Questionnaire and 450 students of the same universities for the Test. Students that participated in the research are studying at the University of Belgrade, University of Novi Sad and University of Niˇs. The results of the research confirmed that students from technological universities have a favourable attitude towards mathematics and that they see its significance in its application, i.e. in its use value. Students have clearly defined attitude on the idea that a good lecture by a professor is one which can be understood, which is well articulated, and which motivates students to take part in it. They point out the significance of examples that have elements of application. Visual presentations also enhance the success in solving problems. The research shows that students did not acquire the skill to apply their knowledge of mathematical analysis in solving tasks and problems. Theoretical clarification of notions of abstraction and application, followed by a displayfive topics of mathematical analysis confirm that abstract theory and applied mathematical analysis are interconnected and conjoint in the universal mathematical system. On the basis of results recommendations are defined concerning innovational approaches to teaching, such as planning the lectures and meliorating the contents, asking questions, and also an intelligent prospect, lecture improvement and learning instruments application. This way, it is confirmed that a methodically well organized lecture helps a better understanding of the relation between abstraction and application of mathematical analysis. URI: http://hdl.handle.net/123456789/4447 Files in this item: 1
doktorska_disertacija_MAlbijanic.pdf ( 4.920Mb ) 
Orlov, Konstantin (Belgrade , 1934)[more][less]

Moconja, Slavko (Beograd , 2015)[more][less]
Abstract: In this thesis we study asymmetric regular types. If p is regular and asymmetric over A, then there exists an order such that Morley sequences in p over A are strictly increasing. It turns out that for every small model M A, the order type of a maximal Morley sequence in p over A whose elements are from M does not depend on the choice of the sequence, i.e. it is an invariant of the model M denoted by Invp;A(M). In the countable case we can determine all possibilities for Invp;A(M): either Invp;A(M) is an arbitrary countable linear order or, provided that it contains at least two elements, it is a countable dense linear order (possibly with one or both endpoints). Also, we study the connection between Invp;A(M) and Invq;A(M), where p and q are two regular and asymmetric over A types such that p A 6?w q A. We distinguish two kinds of nonorthogonality: bounded and unbounded. Under the assumption that p and q are convex, in the bounded case we get that Invp;A(M) and Invq;A(M) are either isomorphic or antiisomorphic, while under the assumption of strong regularity, in the unbounded case we get that Dedekind completions of Invp;A(M) and Invq;A(M) are either isomorphic or antiisomorphic. In particular we study the following class of structures: expansions of linear orderings with countably many unary predicates and countably many equivalence relations with convex classes. We provide new examples of regular types. Namely, it turns out that every global invariant type in this context is regular, and every nonalgebraic type over A has precisely two global extensions which are invariant over A. We also study the connection between the question of existence of a quasi minimal model of a complete rstorder theory and the question of existence of a global strongly regular type. We also deal with the problem whether every quasi minimal group must be abelian. It turns out that this question has the positive answer provided that the global extension of the generic type of a quasiminimal group is asymmetric over ;. URI: http://hdl.handle.net/123456789/4282 Files in this item: 1
phdMoconja_Slavko.pdf ( 2.254Mb ) 
Kadelburg, Zoran (Belgrade)[more][less]

Milošević, Bojana (Beograd , 2016)[more][less]
Abstract: Goodness of t and symmetry tests occupy a signi cant part of nonparametric statistic. Most of classical tests are based on the distance between the assumed distribution function and its consistent estimate, empirical distribution function. The symmetry tests are analogously constructed. A new approach that is especially attractive in recent years is making tests based on characterizations of di erent types. Those tests use Uempirical distribution functions (generalized empirical ones), Uempirical transforms (eg. Laplace transform, characteristic functions etc.) and Uempirical moments of distributions. The main advantage of these tests is that they are often free of some distribution parameters. Therefore they are suitable for testing composite hypothesis. For purpose of comparison of tests the Bahadur e ciency has become very popular. One of the reasons is that it does not require the asymptotic normality of test statistics. In addition, Bahadur and Pitman e ciencies very often locally coincide. It turns out that for determining Bahadur e ciency it is necessary to nd large deviations function under null hypothesis. If that is not possible, usually the approximate Bahadur e ciency is used. It requires the existence of asymptotic distribution and the asymptotic behavior of its tail under null hypothesis, and the limit in probability under alternative distribution. The goals of the thesis are the construction of new goodness of t and symmetry tests based on Ustatistics and V statistics, deriving the asymptotic distribution of proposed statistics, their large deviation functions and Bahadur e ciencies or their approximations. The thesis is divided into two parts. The rst part consists of three chapters. In the rst chapter the theory of Ustatistics and V statistics as well as Uempirical and V empirical distribution function and some other empirical transforms is presented. The second chapter is devoted to the Ustatistics and V statistics with estimated parameters. The third chapter deals with asymptotic e ciency of nonparametric tests. Most of the chapter is devoted to Bahadur e ciency. In the same chapter the large deviation function for a new class of tests statistics is derived. This result is presented in [69]. The second part, which starts with the fourth chapter, is dedicated to new tests based on Ustatistics and V statistics. In the fourth chapter some type of characterizations which are used within the next chapters for construction of tests are presented. They include characterizations based on equidistribution of some statistics among which the characterizations of symmetric distributions stand out, then those based on functional equations that the distribution function satis es, those based on the independence of statistics and those based on moments. Two new characterizations of symmetric distributions are also presented. The fth chapter deals with new goodness of t tests. There are four new exponentiality tests, two new goodness of t tests for a family of Pareto distribution, as well as two new goodness of t tests for logistic distribution (see [66], [69]). Also one new class of uniformity tests which can be used as goodness of t test for any predetermined continuous distribution is proposed (see [67]). The sixth chapter is devoted to new symmetry tests. Five new symmetry tests are proposed. In the seventh chapter there are new exponentiality tests based on Ustatistics and V statistics with estimated parameters. A special attention is given to new tests based on U empirical Laplace transforms. Beside those, some tests based on Uempirical moments are also presented. For new presented tests local Bahadur and/or Pitman e ciency is calculated. In the nal chapter, a brief review of some applications in time series analysis is shown. URI: http://hdl.handle.net/123456789/4470 Files in this item: 1
BojanaMilosevic_doktorat.pdf ( 1.897Mb ) 
Mikić, Marija (Beograd , 2017)[more][less]
Abstract: The subject of this dissertation is the investigation of asymptotic properties of solutions for di erential equations of EmdenFowler type and their generalizations. The eld to which this dissertation belongs is a Qualitative theory of ordinary di e rential equations. EmdenFowler di erential equation has the form (t u0(t))0 t u (t) = 0 ; where ; ; 2 R. With some changes of the variables, this di erential equation can be reduced to the equations y00 xay = 0 and y00 + xay = 0. Firstly, in this dissertation, the di erential equation y00 = xay ; where a; 2 R was observed. The conditions, which provide that this equation has in nitely many solutions de ned in some neighborhood of zero, were described here, both with the conditions, which guarantee the existence of in nitely many solutions with certain asymptotic behavior. Also, a complete picture of asymptotic behavior of solutions of equation along the positive parts of both axes is given. The conditions, which assure existence and unique solvability of solution of the Cauchy problem for this equation, were shown in the cases when the familiar theory can't be applied. In some cases, asymptotic formulas for solutions were obtained. The di erential equation y00 = xay ; where a 2 R i < 0 ; has also been taken into consideration. The conditions, which assure the existence of in nitely many solutions of observed equation tending to zero as x ! 0+, were obtained. The conditions, which assure the unique solvability of the Cauchy problem for generalized EmdenFowler equation y00 = q(x)f(y(x)); lim x!0+ y(x) = 0; lim x!0+ y0(x) = ; were described, for any > 0 and functions f and q which satisfy certain conditions. The given results generalize the results both for sublinear EmdenFowler di erential equation (i.e. case when 0 < < 1) and the case when < 0. In literature, it is very rare to nd the conditions for di erent values of the para metar which appears in the equations of EmdenFowler type. In this dissertation, the results for sublinear and superlinear di erential equation EmdenFowler, as well as the case when < 0, are presented. Therefore, the story of the asymptotic be havior of solutions of the observed equation is "almost complited". URI: http://hdl.handle.net/123456789/4655 Files in this item: 1
Marija_Mikic_disertacija_MTF.pdf ( 1.461Mb ) 
Knežević, Julka (Belgrade)[more][less]

Vujošević Janičić, Milena (Beograd , 2013)[more][less]
Abstract: LAV is a system for statically verifying program assertions and locating bugs such as buffer overflows, pointer errors and division by zero. LAV is primarily aimed at analyzing programs written in the programming language C. Since LAV uses the popular LLVM intermediate code representation, it can also analyze programs written in other procedural languages. Also, the proposed approach can be used with any other similar intermediate low level code representation. System combines symbolic execution, SAT encoding of program’s controlflow, and elements of bounded model checking. LAV represents the program meaning using firstorder logic (FOL) formulas and generates final verification conditions as FOL formulas. Each block of the code (blocks have no internal branchings and no loops) is represented by a FOL formula obtained through symbolic execution. Symbolic execution, however, is not performed between different blocks. Instead, relationships between blocks are modeled by propositional variables encoding transitions between blocks. LAV constructs formulas that encode block semantics once for each block. Then, it combines these formulas with propositional formulas encoding the transitions between the blocks. The resulting compound FOL formulas describe correctness and incorrectness conditions of individual instructions. These formulas are checked by an SMT solver which covers suitable combination of theories. Theories that can be used for modeling correctness conditions are: theory of linear arithmetic, theory of bitvectors, theory of uninterpreted functions, and theory of arrays. Based on the results obtained from the solver, the analyzed command may be given the status safe (the command does not lead to an error), flawed (the command always leads to an error), unsafe (the command may lead to an error) or unreachable (the command will never be executed). If a command cannot be proved to be safe, LAV translates a potential counterexample from the solver into a program trace that exhibits this error. It also extracts the values of relevant program variables along this trace. The proposed system is implemented in the programming language Ñ++, as a publicly available and open source tool named LAV. LAV has support for several SMT solvers (Boolector, MathSAT, Yices, and Z3). Experimental evaluation on a corpus of C programs, which are designed to demonstrate areas of strengths and weaknesses of different verification techniques, suggests that LAV is competitive with related tools. Also, experimental results show a big advantage of the proposed system compared to symbolic execution applied to programs containing a big number of possible execution paths. The proposed approach allows determining status of commands in programs which are beyond the scope of analysis that can be done by symbolic execution tools. LAV is successfully applied in educational context where it was used for finding bugs in programs written by students at introductory programming course. This application showed that in these programs there is a large number of bugs that a verification tool can efficiently find. Experimental results on a corpus of students’ programs showed that LAV can find bugs that cannot be found by commonly used automated testing techniques. Also, it is shown that LAV can improve evaluation of students’s assignments: (i) by providing useful and helpful feedback to students, which is important in the learning process, and (ii) by improving automated grading process, which is especially important to teachers. URI: http://hdl.handle.net/123456789/4231 Files in this item: 1
phdVujosevicJanicicMilena.pdf ( 1.748Mb ) 
Marinković, Vesna (Beograd , 2015)[more][less]
Abstract: The problems of geometry constructions using ruler and compass are one of the oldest and most challenging problems in elementary mathematics. A solution of construction problem is not an illustration, but a procedure that, using given construction primitives, gives a “recipe” how to construct the object sought. The main problem in solving construction problems, both for a human and a computer, is a combinatorial explosion that occurs along the solving process, as well as a procedure of proving solutions correct. In this dissertation a method for automated solving of one class of construction problems, socalled location problems, is proposed. These are the problems in which the task is to construct a triangle if locations of three characteristic points are given. This method successfully proved most of the solvable problems from Wernick’s and Connelly’s list. For each of the problems it is checked if it is symmetric to some of the already solved problems, and then its status is determined: the problem can be found redundant, locus dependent, solvable, or not solvable using existing knowledge. Also, a description of the construction in naturallanguage form and in language GCLC is automatically generated, accompanied by a corresponding illustration, and correctness proof of the generated construction, followed by the list of conditions when the construction is correct. The proposed method is implemented within the tool ArgoTriCS. For proving generated constructions correct, the system ArgoTriCS uses a newly developed prover ArgoCLP, the automated theorem provers integrated within tools GCLC and OpenGeoProved, as well as the interactive theorem prover Isabelle. It is demonstrated that the proofs obtained can be machine verifiable. Within this dissertation, the system ArgoCLP (developed in collaboration with Sana Stojanovi´c) which is capable of automatically proving theorems in coherent logic is described. This prover is successfully applied to different axiomatic systems. It automatically generates proofs in naturallanguage form, as well as machineverifiable proofs, whose correctness can be checked using interactive theorem prover Isabelle. The important part of this system is a module for simplification of generated proofs whereby shorter and readable proofs are obtained. URI: http://hdl.handle.net/123456789/4406 Files in this item: 1
tezaVesnaMarinkovic.pdf ( 2.233Mb ) 
Tasković, Milan (Belgrade)[more][less]

PavlovićLažetić, Gordana (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/45 Files in this item: 1
phdGordanaPavlovicLazetic.pdf ( 4.791Mb ) 
IlićDajović, Milica (Belgrade , 1965)[more][less]

Leko, Marko (Belgrade , 1963)[more][less]

Leko, Marko (Beograd , 1980)[more][less]

Atanasijević, Ksenija (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/183 Files in this item: 1
phdKsenijaAtanasijevic.pdf ( 1.987Mb ) 
Arsenović, Mihajlo (Belgrade)[more][less]

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

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

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