Browsing Mathematics by Title

ŠeganRadonjić, Marija (University of Belgrade , 2019)[more][less]
Abstract: Предмет докторске дисертације је израда оквира за дигитално архивирање у циљу очувања, представљања и омогућавања доступности дигитализованог и дигиталног садржаја за потребе историјских и других истраживања. Предложени оквир заснива се на концепту ,,тематских колекција“ и намењен је истраживачима који желе да креирају сопствене дигиталне збирке историјских извора и текстова како би ширу научну заједницу упознали са својим истраживањем, повезали га са ширим контекстом и створили услове за умрежавање и сарадњу. Оквир, на примеру дигитализације архивског материјала Математичког института САНУ и у складу са актуелним препорукама и прописима за дигитализацију културног наслеђа у Републици Србији, нуди смернице за: 1) економичан поступак превођења у дигитални облик ради добијања оперативних копија за представљање на вебу, 2) каталогизацију и опис дигиталних докумената помоћу Dublin Core скупа елемената, 3) креирање дигиталног архива помоћу Omeka Classic платформе, 4) израду упутства за архивско истраживање одређених историјских тема и 5) састављање историјских есеја у дигиталном окружењу. Посебни циљ докторске дисертације је примена предложеног оквира у историјским и другим истраживањима, конкретно у проучавању развоја Математичког института у периоду од његовог успостављања у крилу Српске академије наука 1946. године до његовог осамостаљивања 1961. године. Резултати рада су: 1) систематски обрађено питање прошлости Математичког института САНУ у поменутом хронолошком оквиру, 2) дигитална колекција посвећена историји математике и сродних наука у Србији и југоисточној Европи и 3) предлог оквира за дигитално архивирање дигиталног и дигитализованог садржаја за потребе историјских и других истраживања. URI: http://hdl.handle.net/123456789/4855 Files in this item: 1
MarijaSeganDoktorat.pdf ( 29.70Mb ) 
Borisavljević, Mirjana (Beograd , 1997)[more][less]

Bakić, Radoš (Belgrade)[more][less]

Mijajlović, Ivana (London)[more][less]

Pavlović, Aleksandar (Novi Sad)[more][less]
URI: http://hdl.handle.net/123456789/295 Files in this item: 1
PhdAleksandarPavlovic.pdf ( 7.226Mb ) 
Đokić, Dragan (Beograd , 2022)[more][less]
Abstract: The distribution of primes is determined by the distribution of zeros of Riemann zeta function, and indirectly by the distribution of magnitude of this function on the critical line <s = 1 2 . Similarly, in order to consider the distribution of primes in arithmetic progressions, Dirichlet introduced Lfunctions as a generalization of Riemann zeta function. Generalized Riemann hypothesis, the most important open problem in mathematics, predicts that all nontrivial zeros of Dirichlet Lfunction are located on the critical line. Therefore, one of the main goals in Analytic Number Theory is to consider the moments of Dirichlet Lfunctions (according to a certain well defined family). The relation with the characteristic polynomials of random unitary matrices is one of the fundamental tools for heuristic understanding of Lfunctions and derivation hypotheses about asymptotic formulae for their moments. Asymptotics for even moments 1 T Z T 0 ζ 1 2 + it 2k dt, as T → ∞, is still an open question (except for k = 1, 2), and it is related to the Lindelöf Hypothesis. In this dissertation we consider the sixth moment of Dirichlet Lfunctions over rational function fields Fq(x), where Fq is a finite field. We will present the asymptotic formula for the sixth moment with the triple average X Q monic deg Q=d X χ (mod Q) χ odd primitive 2π Z log q 0 L 1 2 + it, χ 6 dt 2π log q as d → ∞. All additional averaging is currently necessary to obtain the asymptotics. The summation over Dirichlet characters and their moduli is motivated by BombieriVinogradov Theorem. Our result is a function field analogue of the paper [25] for the corresponding family and averaging over field Q. Also, our main term confirms the existing Random matrix theory predictions. URI: http://hdl.handle.net/123456789/5531 Files in this item: 1
dragan_djokic_teza.pdf ( 867.8Kb ) 
Pogany, Tibor (Belgrade)[more][less]

Todorović, Petar (Belgrade , 1961)[more][less]

Ikodinović, Nebojša (Kragujevac)[more][less]
Abstract: The thesis is devoted to logics which are applicable in different areas of mathematics (such as topology and probability) and computer sciences (reasoning with uncertainty). Namely, some extensions of the classical logic, which are either modeltheoretical or nonclassical, are studied. The thesis consists of three chapters: an introductory chapter and two main parts (Chapter 2 and Chapter 3). In the introductory chapter of the thesis the wellknown notions and properties from extensions of the first order logic and nonclassical logics are presented. Chapter 2 of the thesis is related to logics for topological structures, particularly, topological class spaces (topologies on proper classes). One infinite logic with new quantifiers added is considered as the corresponding logic. Methods of constructing models, which can be useful for many others similar logics, are used to prove the completeness theorem. A number of probabilistic logic suitable for reasoning with uncertainty are investigated in Chapter 3. Especially, some ways of incorporation into the realm of logic conditional probability understood in different ways (in the sense of Kolmogorov or De Finnety) are given. For all these logics the corresponding axiomatizations are given and the completeness for each of them is proved. The decidability for all these logics is discussed too. URI: http://hdl.handle.net/123456789/194 Files in this item: 1
phdNebojsaIkodinovic.pdf ( 3.008Mb ) 
Ognjanović, Zoran (Kragujevac)[more][less]
Abstract: The thesis consists of seven chapters and two appendixes. The Chapter 1 and the appendixes contain known notions and properties from probability logics. In Chapter 2 some propositional probability logics are introduced and their languages, models, satisfiability relations, and (in)finitary axiomatic systems are given. Object languages are countable, formulas are finite, while only proofs are allowed to be infinite. The considered languages are obtained by adding unary probabilistic operators of the form P≥s. Decidability of the logics is proved. In Chapter 3 some first order probability logics are considered while in Chapter 4 new types of probability operators are introduced. The new operators are suitable for describing events in discrete sample spaces. It is shown that they are not definable in languages of probability logics that have been used so far. A propositional and a firstorder logic for reasoning about discrete linear time and finitely additive probability are given in Chapter 5. Sound and complete infinitary axiomatizations for the logics are provided as well. In Chapter 6 a probabilistic extension of modal logic is studied and it is shown that those logics are closely related, but that modal necessity is a stronger notion than probability necessity. In Chapter 7 decidability of these logics is shown by reducing the corresponding satisfiability problem to the linear programming problem. Finally, two automated theorems provers based on that idea are described. URI: http://hdl.handle.net/123456789/197 Files in this item: 1
phdZoranOgnjanovic.pdf ( 1.259Mb ) 
Shkheam, Abejela (, 2013)[more][less]
Abstract: This thesis has been written under the supervision of my mentor, Prof. dr. Milo s Arsenovi c at the University of Belgrade academic, and my comentor dr. Vladimir Bo zin in year 2013. The thesis consists of three chapters. In the rst chapter we start from de nition of harmonic functions (by mean value property) and give some of their properties. This leads to a brief discussion of homogeneous harmonic polynomials, and we also introduce subharmonic functions and subharmonic behaviour, which we need later. In the second chapter we present a simple derivation of the explicit formula for the harmonic Bergman reproducing kernel on the ball in euclidean space and give a proof that the harmonic Bergman projection is Lp bounded, for 1 < p < 1, we furthermore discuss duality results. We then extend some of our previous discussion to the weighted Bergman spaces. In the last chapter, we investigate the Bergman space for harmonic functions bp, 0 < p < 1 on RnnZn. In the planar case we prove that bp 6= f0g for all 0 < p < 1. Finally we prove the main result of this thesis bq bp for n=(k + 1) q < p < n=k, (k = 1; 2; :::). This chapter is based mainly on the published paper [44]. M. Arsenovi c, D. Ke cki c,[5] gave analogous results for analytic functions in the planar case. In the plane the logarithmic function log jxj, plays a central role because it makes a di erence between analytic and harmonic case, but in the space the function jxj2n; n > 2 hints at the contrast between harmonic function in the plane and in higher dimensions. URI: http://hdl.handle.net/123456789/3053 Files in this item: 1
phd_Shkheam_Abejela.pdf ( 650.6Kb ) 
Tepavčević, Andreja (Novi Sad)[more][less]

Bulatović, Jelena (Belgrade)[more][less]

Borovićanin, Bojana (Kragujevac, Serbia , 2008)[more][less]
Abstract: Different spectral characterizations of certain classes of graphs are considered in this dissertation. The large number of papers concerning this topic, indicates that problems of this kind are very interesting in spectral graph theory. This dissertation, beside Preface and References with 46 items, consists of two chapters: 1. Harmonic graphs, 2. Graphs with maximal index. Harmonic graphs are introduced and studied in details in Chapter 1. This chapter consists of four sections. In section 1.1 the definition of harmonic graphs, as well as their basic properties, are given. Harmonic trees are discussed in section 1.2. In section 1.3 we characterize harmonic graphs with small number of cycles; in particular, all unicyclic, bicyclic, tricyclic and tetracyclic graphs are determined. Finally, in section 1.4, we determine all connected 3harmonic graphs with integral spectrum. The solution of maximal index problem in certain classes of graphs is given in Chapter 2. This chapter consists of four sections. In sections 2.1 and 2.2 we review some results related to the index of a graph. The emphasis is on graphs with given number of both vertices and edges; in particular we discuss graphs having the fixed number of pendant edges, too. In section 2.3 we give the solution of maximal index problem in the class of connected tricyclic graphs with n vertices and k pendant edges. Finally, in section 2.4, we determine graphs with maximal index among all connected cactuses with n vertices. URI: http://hdl.handle.net/123456789/1834 Files in this item: 1
disertacija_Bojana Borovicanin.pdf ( 1.939Mb ) 
Jovanović, Irena (Beograd , 2014)[more][less]
Abstract: Spectral graph theory is a mathematical theory where graphs are considered by means of the eigenvalues and the corresponding eigenvectors of the matrices that are assigned to them. The spectral recognition problems are of particular interest. Between them we can distinguish: characterizations of graphs with a given spectrum, exact or approximate constructions of graphs with a given spectrum, similarity of graphs and perturbations of graphs. In this dissertation we are primarily interested for the similarity of graphs, where graphs with the same number of vertices and graphs of different orders are considered. Similarity of graphs of equal orders can be established by computation of the spectral distances between them, while for graphs with different number of vertices the measures of similarity are introduced. In that case, graphs under study are usually very large and they are denoted as networks, while the measures of similarity can be spectraly based. Some mathematical results on the Manhattan spectral distance of graphs based on the adjacency matrix, Laplacian and signless Laplacian matrix are given in this dissertation. A new measure of similarity for the vertices of the networks under study is proposed. It is based on the difference of the generating functions for the numbers of closed walks in the vertices of networks. These closed walks are calculated according to the new spectral formula which enumerates the numbers of spanning closed walks in the graphlets of the corresponding graphs. The problem of the characterization of a digraph with respect to the spectrum of AAT , apropos ATA, where A is the adjacency matrix of a digraph, is introduced. The notion of cospectrality is generalized, and so the cospectrality between some particular digraphs with respect to the matrix AAT and multigraphs with respect to the signless Laplacian matrix is considered. URI: http://hdl.handle.net/123456789/4233 Files in this item: 1
Jovanović_Irena.pdf ( 1.138Mb ) 
Adamović, Dušan (Belgrade , 1965)[more][less]

Algali, Khola (Beograd , 2019)[more][less]
Abstract: In this thesis we give some new asymptotic formulas for mean values of multiplicative functions of several variables depending on GCD and LCM of arguments. We obtain an asymptotic formula with a power saving error term for the summation function of a family of generalized least common multiple and greatest common divisor functions of several integer variables. Xn 1,...,nk+`≤x [n1,...,nk]a (n1,...,nk)c , [nk+1,...,nk+`]b (nk+1,...,nk+`)d = Ck,a,c;`,b,d (a + 1)k(b + 1)` xk(a+1)+`(b+1) + O xk(a+1)+`(b+1)−1 2+ and Xn 1,...,nk+`≤x [n1,...,nk]a (n1,...,nk)c , [nk+1,...,nk+`]b (nk+1,...,nk+`)d (n1 ...nk)a(nk+1 ...nk+`)b = Ck,a,c;`,b,d xk+` + O xk+`−1 2+ . Also we obtain an asymptotic formula with a power saving error term for the summation function of Euler phifunction evaluated at iterated and generalized least common multiples of four integer variables. Xn 1,n2,n3,n4≤x ϕ [n1,n2]a (n1,n2)c , [n3,n4]b (n3,n4)d = Ca,c;b,d (a + 1)2(b + 1)2 x2a+2b+4 + O x2a+2b+7 2+ . URI: http://hdl.handle.net/123456789/4820 Files in this item: 1
khola_phd_new_ver.pdf ( 665.4Kb ) 
Ranković, Dragana (Beograd , 2011)[more][less]

Alidema, Rašit (Belgrade , 1980)[more][less]

Nikolić, Nebojša (Beograd , 2015)[more][less]
Abstract: A Steiner system S(t; k; v) is a set which contains v elements (vset) and a family of ksubsets (blocks), such that each tsubset appears in exactly one block (v > k > t > 1; v; k; t 2 N). In the case of a (v; k; t)¡covering, each tsubset appears in at least one block of a given family. A Steiner system S(t; k; v) exists if and only if C(v; k; t) = ¡v t ¢±¡k t ¢ , where C(v; k; t) is the cardinality of minimal (v; k; t)¡covering. As the existence of Steiner system S(t; k; v) and the determination of the minimal (v; k; t)¡covering are still open problems, their solutions are known only in some special cases. Besides the review of the previous results related to the problem of the existence of Steiner systems and the problem of determining the minimal (v; k; t)¡covering, several new constructions of (v; k; t)¡covering are given in this paper. Since the number of blocks in (v; k; t)¡covering represents the upper bound on C(v; k; t), a large number of upper bounds are also obtained by using these constructions. In many cases, the obtained upper bounds are better than the best known upper bounds on C(v; k; t). This dissertation gives a new combinatorial construction of minimal (v; 3; 2)¡ coverings, which represents a generalization of Bose and Skolem constructions of the Steiner triple systems STS(6n + 3) and STS(6n + 1). In each of the 6 cases (v = 6n; : : : ; 6n+5), (v; 3; 2)¡covering is obtained by applying certain permutation p to the initial set of blocks. The obtained construction also represents a new proof of the statement that the values of C(v; 3; 2) are equal to SchÄonheim lower bound L(v; 3; 2). Other constructions of (v; k; t)¡coverings, given in this paper, are heuristic. First, we give improved implementation of the well known greedy algorithm. Then, a new greedy algorithm, as well as the theorem which provides a su±cient con dition for equality of greedy lex and greedy colex coverings are given. Finally, by v using so called LR procedure, three other heuristics are developed and implemented: Large neighbourhood search, Variable neighborhood descent and General variable neighborhood search. Large neighbourhood search is the procedure of alternately destroying and re pairing a solution in order to improve the incumbent solution. In the proposed algorithm, this is the procedure for systematic removing and adding blocks to the covering, based on LR procedure. By using LR procedure, the blocks which exclu sively cover the minimal number of tsubsets are removed from (v; k; t)¡covering, and then the uncovered tsubsets are covered with as few blocks as possible. The greedy algorithm is used for the covering of the uncovered tsubsets. Variable neighborhood search is based on the idea of systematic change of neigh borhood within a local search algorithm in order to avoid the convergence to a local minimum. A variant of the method where changes of neighborhood is performed in a deterministic way is called Variable neighborhood descent. A variant where the local search procedure is replaced by the Variable neighborhood descent method is General variable neighborhood search. The basis of the local search procedure applied in these two heuristics is also LR procedure. Regarding quality of the obtained results and the performance of the methods, Large neighbourhood search, Variable neighborhood descent, and General variable neighborhood search overcome two heuristics for solving the problem of minimal (v; k; t)¡covering known from the literature: Simulated annealing and Tabu search. Unlike the existing heuristics, the proposed heuristics are applicable to arbitrarily (v; k; t)¡covering. By applying aforementioned heuristics, 23 new best known upper bounds on C(v; k; t) are established. URI: http://hdl.handle.net/123456789/4285 Files in this item: 1
phdNikolic_Nebojsa.pdf ( 851.1Kb )