Browsing Mathematics by Title
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Damjanović, Boško (Belgrade)[more][less]
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Milošević, Nela (Beograd , 2015)[more][less]
Abstract: This dissertation examines simplicial complexes associated with commutative rings with unity. In general, a combinatorial object can be attached to a ring in many di erent ways, and in this dissertation we examine several simplicial complexes attached to rings which give interesting results. Focus of this thesis is determining the homotopy type of geometric realization of these simplicial complexes, when it is possible. For a partially ordered set of nontrivial ideals in a commutative ring with identity, we investigate order complex and determine its homotopy type for the general case. Simplicial complex can also be associated to a ring indirectly, as an independence complex of some graph or hypergraph which is associated to that ring. For the comaximal graph of commutative ring with identity we de ne its independence complex and determine its homotopy type for general commutative rings with identity. This thesis also focuses on the study of zero-divisors, by investigating ideals which are zero-divisors and de ning zero-divisor ideal complex. The homotopy type of geometric realization of this simplicial complex is determined for rings that are nite and for rings that have in nitely many maximal ideals. In this part of the thesis, we use the discrete Morse theory for simplicial complexes. The theorems proven in this dissertation are then applied to certain classes of commutative rings, which gives us some interesting combinatorial results. URI: http://hdl.handle.net/123456789/4421 Files in this item: 1
Nela_Milosevic_Teza.pdf ( 20.62Mb ) -
Cvetković, Milica (Niš , 2013)[more][less]
Abstract: This work provides the surface shape analysis in R3 using the shape operator, i.e. using the curvatures as well as curvature's functionals such as the Willmore energy. Then, there were considered changes of surfaces' geometric characteristics under infinitesimal deformations, and specialy, curvature based functionals variations under infinitesimal bending of surface. Special kinds of ruled surfaces were analysed from geometrical and constructional point of view, and pointed to their wide use. At last, there is a generalization by considering the Finsler and the generalized Finsler spaces. URI: http://hdl.handle.net/123456789/3813 Files in this item: 1
2014_01_22_cm.pdf ( 1.476Mb ) -
Ilić, Dejan (Beograd , 2016)[more][less]
Abstract: We study linearly ordered structures and their complete theories. The main technical tools used in the analysis are condensations, i.e. partitioning the ordering into convex parts and then studying the quotient structure and that of the parts. We introduce a uniformly definable condensation relation cδ that decomposes the ordering into largest convex pieces whose first order theory is simple: they are either dense or discrete orderings. We study cδ quotient structures that are expansions of certain simple countable discrete orderings and give a precise description of those having Cantor Bendixson rank 1. We also use the condensation cδ to prove that any linear ordering expanded by finitely many unary predicates and equivalence relations with convex classes is interpretable in a pure linear ordering. We introduce notions of linear and strong linear binarity for linearly ordered structures and their complete theories. In the case of a theory, the defining condition expresses a property of the automorphism group of its saturated model. We prove that any complete theory of a linear ordering with unary predicates and equivalence relations with convex classes is strongly linearly binary. The main result states that a strongly linearly binary structure is definitionally equivalent to a linear ordering with unary predicates and equivalence relation with convex classes added. In the proof we give a description of definable sets in any linear ordering with unary predicates and equivalence relations with convex classes. URI: http://hdl.handle.net/123456789/4452 Files in this item: 1
disertacija_IlicDejan.pdf ( 756.7Kb ) -
Pucanović, S. Zoran (Belgrade , 2012)[more][less]
Abstract: This dissertation examines various properties of commutative rings and modules using algebraic combinatorial methods. If the graph is properly associated to a ring R or to an R-module M, then examination of its properties gives useful information about the ring R or R-module M. This thesis discusses the determination of the radius of the total graph of a commutative ring R in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the R-module M and relations between the total graph of the ring R and its extensions are also dealt with. The total graph of a module, a generalization of the total graph of a ring is presented. Various properties are proved and some relations to the total graph of a ring as well as to the zero-divisor graph are established. To gain a better understanding of clean rings and their relatives, the clean graph C¡(R) of a commutative ring with identity is introduced and its various proper- ties established. Further investigation of clean graphs leads to additional results concerning other classes of commutative rings. One of the topics of this thesis is the investigation of the properties of the cor- responding line graph L(T¡(R)) of the total graph T¡(R). The classi¯cation of all commutative rings whose line graphs of the total graph are planar or toroidal is given. It is shown that for every integer g ¸ 0 there are only ¯nitely many commutative rings such that °(L(T¡(R))) = g. Also, in this thesis all toroidal graphs which are intersection graphs of ideals of a commutative ring R are classi¯ed. An improvement over the previous results concerning the planarity of these graphs is presented. URI: http://hdl.handle.net/123456789/2489 Files in this item: 1
Pucanovic_Zoran.pdf ( 2.059Mb ) -
Radunović, Desanka (Belgrade , 1984)[more][less]
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Šarović, Jovo (Belgrade)[more][less]
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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 Fixed-Point 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]
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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 non-orthogonality: 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 anti-isomorphic, 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 anti-isomorphic. 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 non-algebraic 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 rst-order 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 quasi-minimal 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]
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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 U-empirical distribution functions (generalized empirical ones), U-empirical transforms (eg. Laplace transform, characteristic functions etc.) and U-empirical 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 U-statistics 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 U-statistics and V -statistics as well as U-empirical and V -empirical distribution function and some other empirical transforms is presented. The second chapter is devoted to the U-statistics 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 U-statistics 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 U-statistics 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 U-empirical 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 Emden-Fowler type and their generalizations. The eld to which this dissertation belongs is a Qualitative theory of ordinary di e- rential equations. Emden-Fowler 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 Emden-Fowler 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 Emden-Fowler 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 Emden-Fowler type. In this dissertation, the results for sublinear and superlinear di erential equation Emden-Fowler, 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]
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Timotijević, Marinko (Beograd , 2019)[more][less]
URI: http://hdl.handle.net/123456789/4818 Files in this item: 1
Disertacija_Marinko_Timotijevic.pdf ( 1.189Mb ) -
Tasković, Milan (Belgrade)[more][less]
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Pavlović-Lažetić, Gordana (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/45 Files in this item: 1
phdGordanaPavlovicLazetic.pdf ( 4.791Mb ) -
Ilić-Dajović, Milica (Belgrade , 1965)[more][less]
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Zekić, Mladen (Beograd , 2021)[more][less]
Abstract: Central place in this thesis occupy the coherence results for certain types of closed categories. Coherence results in category theory usually serve to provide a simple decision procedure for equality of arrows in some category. The approach to coherence that we follow here implies the existence of a faithfull functor from a freely generated category A of certain type to the category B in which an equality of arrows can be easily checked. Category B, which is of the same type as A, usually represents formalisation of some graphical language. Besides coherence, the second most important notion we consider in this thesis is the biproduct. The notion of biproduct in a category incorporates notions of coproduct and product. The main results in this thesis are coherence theorems for three types of closed categories with biproducts – symmetric monoidal closed categories with biproducts, com- pact closed categories with biproducts and dagger compact closed categories with dagger biproducts. Further, we present a new proof of the well-known Kelly-Mac Lane coherence theorem for symmetric monoidal closed categories. The methods we use in that proof are completely proof-theoretical, and one of the key elements in it is the cut-elimination theorem. In all the above coherence results, the graphical language is based on the category of one-dimensional cobordisms. Finaly, we give certain criteria for existence of biproducts in monoidal categories. In this regard, we rely on recent research that characterizes certain type of monoidal categories with finite biproducts by using the existence of right duals of some distinguished objects. Our criteria are a generalization of this result. URI: http://hdl.handle.net/123456789/5307 Files in this item: 1
mladen.zekic.disertacija.pdf ( 1.018Mb )