Browsing Mathematics by Issue Date
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Stanimirović, Zorica (Belgrade , 2007)[more][less]
Abstract: U ovom radu opisani su različiti genetski algoritmi (GA) za rešavanje četiri NP-teška hab lokacijska problema: problem p-hab medijane neograničenih kapaciteta sa jednostrukim alokacijama (USApHMP), problem p-hab medijane/centra ograničenih kapaciteta sa jednostrukim alokacijama (CSApHMP/CSApHCP) i hab lokacijski problem ograničenih kapaciteta sa jednostrukim alokacijama (CSAHLP). Ovi hab lokacijski problemi nalaze veliku primenu u dizajniranju transportnih i telekomunikacijskih sistema, poštanskih i drugih sistema isporuke, lokalnih i globalnih računarskih mreža, itd. Za problem p-hab medijane neograničenih kapaciteta sa jednostrukim alokacijama (USApHMP), razvijene su GA metode koje koriste dva različita načina kodiranja i adekvatne modifikovane genetske operatore. U cilju poboljšanja efikasnosti predloženih genetskih algoritama, primenjena je hibridizacija oba GA koncepta sa heuristikom lokalnog pretraživanja, pa su tako nastale hibridne HGA1 i HGA2 metode koje su veoma uspešne i pri rešavanju problema velikih dimenzija. Za rešavanje hab lokacijskih problema ograničenih kapaciteta CSApHMP, CSApHCP i CSAHLP takođe su predložene razne verzije genetskih algoritama. Primenjene su dve razičite reprezentacije rešenja i odgovarajući genetski operatori razvijeni u skladu sa prirodom problema. Implementirani genetski operatori čuvaju korektnost jedinki u tokom generacija GA i u smislu očuvanja broja uspostavljenih habova i u smislu ograničenja kapaciteta habova. Sve opisane genetske (evolutivne) metode testirane su na odgovarajućim standardnim ORLIB instancama iz literature. Za sva četiri hab lokacijska problema koja su razmatrana u ovom radu, predloženi (hibridni) genetski algoritmi dostižu sve do sada poznate optimalne vrednosti na datim instancama u zadovoljavajućem vremenu izvršavanja. U radu su data rešenja i za probleme velikih dimenzija (n=100,200 p≤20) za koje optimalna rešenja nisu poznata, a neki od ovih problema do sada nisu rešavani u literaturi. Dobijeni rezultati predloženih GA metoda jasno ukazuju na značaj i potencijal genetskih pristupa rešavanju hab i drugih lokacijskih problema.In this paper some new genetic algorithms (GA) for solving four NP-hard hub location problems are described: Uncapacitated Single Allocation p-hub Center Problem (USApHCP), Capacitated Single Allocation p-hub Median/Center Problem (CSApHMP/CSApHCP) and Capacitated Single Allocation Hub Location Problem (CSAHLP). These hub ploblems have various applications in designing transportation and telecommunications systems, postal and other delivery systems, local and golobal computer area networks, etc. For the Uncapacitated Single Allocation p-hub Center Problem (USApHCP), two hybrid heuristic methods, named HGA1 and HGA2 are proposed. These methods are a combination of a genetic algorithm and a generalization of the well-known fast interchange heuristic (IH). In order to investigate the effect of encoding on GA performance, two different encoding schemes are implemented: binary encoding in HGA1, and integer representation in HGA2. Modified genetic operators that keep the feasibility of individuals are designed and implemented in both HGA1 and HGA2. The performed computational experiments showed the effectiveness of both hybrid methods, even for solving large-scaled problem instances For the capacitated variants of hub location problems CSApHMP, CSApHCP i CSAHLP, new genetic approaches are also described. In proposed genetic algorithms, new encoding schemes are implemented with appropriate objective functions. By using specific representation and modified genetic operators, proposed GA approaches keep the feasibility of individuals, i.e. the fixed number of established hubs and/or satisfying the capacity constraints on hubs. The numerical experiments were carried out on the standard hub data set from the literature. For all four hub problems that were studied, the corresponding GA method proved to be robust and efficient in solving the problem instances with up to 200 nodes and 20 hubs. Computational experiments demonstrate that all proposed GA methods reach all previously known optimal solutions on tested hub instances. The algorithm is also benchmarked on large scale hub instances with n=100,200 nodes and p≤20 hubs that are not solved (to optimality) so far. The presented computational results clearly indicate the usefulness of the proposed GA approaches. URI: http://hdl.handle.net/123456789/298 Files in this item: 1
phdZoricaStanimirovic.pdf ( 666.6Kb ) -
Stanić, Marija (Kragujevac, Srbija , 2007)[more][less]
Abstract: The field of research in this dissertation is consideration of some nonstandard types of orthogonality and their applications to constructions of quadrature rules with maximal degree of exactness, i.e., quadrature rules of Gaussian type. The research in this dissertation is connected with the following subjects: Theory of Orthogonality, Numerical Integration and Approximation Theory. We have tried to produce a balanced work between theoretical results and numerical algorithms. URI: http://hdl.handle.net/123456789/1741 Files in this item: 1
PhD MS.pdf ( 784.9Kb ) -
Manojlović, Vesna (Beograd , 2008)[more][less]
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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 3-harmonic 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 ) -
Božović, Vladimir (Boca Raton, Florida , 2008)[more][less]
Abstract: The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed. URI: http://hdl.handle.net/123456789/296 Files in this item: 1
phdVladimirBozovic.pdf ( 1.070Mb ) -
Stankov, Dragan (Belgrade , 2008)[more][less]
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Šobot, Boris (Novi Sad , 2009)[more][less]
Abstract: The method of forcing is widely used in set theory to obtain various consistency proofs. Complete Boolean algebras play the main role in applications of forcing. Therefore it is useful to define games on Boolean algebras that characterize their properties important for the method. The most investigated game is Jech’s distributivity game, such that the first player has the winning strategy iff the algebra is not (!, 2)-distributive. We define another game characterizing the collapsing of the continuum to !, prove several sufficient conditions for the second player to have a winning strategy, and obtain a Boolean algebra on which the game is undetermined. URI: http://hdl.handle.net/123456789/297 Files in this item: 1
phdBorisSobot.pdf ( 987.6Kb ) -
Šobot, Boris (UNIVERSITY OF NOVI SAD FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS AND INFORMATICS , 2009)[more][less]
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Zlatanović, Milan (Niš , 2010)[more][less]
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Andrejić, Vladica (Beograd , 2010)[more][less]
Abstract: U ovom radu posmatramo princip dualnosti (i jake dualnosti) za Osermanove mnogostrukosti i uopxtavamo ga za pseudo-Rimanov sluqaj. Osnovni ci je dokazati princip dualnosti za Osermanove mnogostrukosti u opxtem sluqaju ili konstrukcija eventualnih kon- traprimera. Za sada smo u sta u da damo samo rezultate pod speci- fiqnim dodatnim uslovima. Prva mogu nost je mali indeks pseudo- Rimanove mnogostrukosti, gde dokazujemo da jaka dualnost va i za Rimanove i Lorencove prostore. Druga mogu nost su prostori malih dimenzija gde dokazujemo da jaka dualnost va i kad dimenzija nije ve a od qetiri. Posled a olakxavaju a okolnost sa kojom radimo tiqe se malog broja sopstvenih vrednosti redukovanog Jakobijevog operatora, gde posmatramo dvolisno-Osermanove tenzore krivine. U tom sluqaju radimo sa jakim uslovima iz definicije kvazi-specijalnih Osermanovih tenzora krivine i elimo da doka emo da pod ima va i princip dualnosti. Konaqan rezultat je da skoro-specijalan Oser- manov tenzor krivine mora biti specijalan Osermanov. U nastavku postav amo obratan problem, te pokuxavamo da istra imo pod kojim uslovima algebarski tenzor krivine za koji va i princip dualnosti mora biti Osermanov. Potvrdan rezultat dobili smo u dimenziji tri, kao i u sluqaju kada se Fidlerova suma sastoji od samo jednog qlana. URI: http://hdl.handle.net/123456789/2479 Files in this item: 1
phdAndrejicVladica.pdf ( 513.6Kb ) -
Vučković, Vesna (Univerzitet u Beogradu – Matematički fakultet , 2010)[more][less]
Abstract: This dissertation deals with digital watermark for grayscale images. Digital watermark in copyright protection needs to satisfy detectability and fidelity conditions. If watermark is embedded stronger, it will be likely detectable, but it will be noticeable too, and it will jeopardize host image quality. Here, for a well known, AWGN watermark, optimal embedding strength (minimal which guaranties watermark detectability) is determined. Optimal strength is analyzed - for effective embedding (watermark needs to be detectable immediately after embedding) - for watermark to be robust against expected modification (it needs to be detectable in image which will be after embedding subjected to this modification) For effective AWGN watermark embedding, mathematical formula for optimal strength calculating is derived. For watermark robust against expected modification, one algorithm for optimal strength is given. Among all image modifications (valumetric and geometric), lossy compression surely has an important place. Images which nowadays we can find on Net are mostly in some lossy compressed form. In such circumstances, embedded watermark will also surely be exposed to lossy compression. This is why in this dissertation particular attention is devoted to lossy compression. Thus, its considerable part deals with AWGN watermark optimal strength, in spatial and in transform domains. Specially, here is analyzed embedding in some image subchannels in the block DCT domain, and quantization noise impact on the embedded watermark message. URI: http://hdl.handle.net/123456789/1073 Files in this item: 1
PhDVVuckovic.pdf ( 4.249Mb ) -
Levajković, Tijana (Novi Sad , 2011)[more][less]
Abstract: In this dissertation we study the main properties of the operators of Malliavin calculus de ned on a set of singular generalized stochastic processes, which admit chaos expansion representation form in terms of orthogonal polynomial basis and having values in a certain weighted space of stochastic distributions in white noise framework. In the rst part of the dissertation we focus on white noise spaces and introduce the fractional Poissonian white noise space. All four types of white noise spaces obtained (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian) can be identi ed through unitary mappings. As a contribution to the Malliavin di erential theory, theorems which characterize the operators of Malliavin calculus, extended from the space of square integrable random variables to the space of generalized stochastic processes were obtained. Moreover the connections with the corresponding fractional versions of these operators are emphasized and proved. Several examples of stochastic di erential equations involving the operators of the Malliavin calculus, solved by use of the chaos expansion method, have found place in the last part of the dissertation. Particularly, obtained results are applied to solving a generalized eigenvalue problem with the Malliavin derivative and a stochastic Dirichlet problem with a perturbation term driven by the Ornstein-Uhlenbeck operator. URI: http://hdl.handle.net/123456789/3824 Files in this item: 1
DR_Tijana.pdf ( 1.518Mb ) -
Gardašević Filipvić, Milanka (Beograd , 2011)[more][less]
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Doder, Dragan (Beograd , 2011)[more][less]
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Ranković, Dragana (Beograd , 2011)[more][less]
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Marinković, Silvana (Kragujevac, Serbia , 2011)[more][less]
Abstract: In this dissertation functions and equations in some classes of lattices such as Post algebras, Stone algebras and multiple-valued logics, are studied. The dissertation, beside Preface and References with 46 items, consists of five chapters. In Introduction some basic notations which will be used in next chapters are given. Main results on Boolean functions and equations are exposed in Chapter 2. In Chapter 3, assuming that a general solution is known, the class of reproductive general solutions of the equation in Stone algebra is described. All general solutions of equations in one variable in multiple-valued logic are described in Chapter 4. A necessary and sufficient conditions that given sequence of recurrent inequalities represents solution of some consistent Post equation are given in Chapter 5. Also, it is proved that every Post transformation is the parametric solution of some consistent Post equation. URI: http://hdl.handle.net/123456789/1842 Files in this item: 1
SilvanaMarinkovicDoktorat.pdf ( 360.3Kb ) -
Lazić, Mirjana (Kragujevac, Serbia , 2011)[more][less]
Abstract: This doctoral dissertation belongs to the Spectral theory of finite and infinite graphs, which joins elements of Graph theory and Linear algebra. The dissertation, beside Preface and References with 24 items, consists of four chapters divided in sections and Appendix. In Chapter 1 some results on the reduced energy of graphs are given. All connected graphs whose reduced energy does not exceed 3 are described. In Chapter 2 all finite and infinite graphs with seven nonzero eigenvalues are determined. Some results on integral graphs are given in Chapter 3. Finally, Chapter 4 contains some results on symmetric double starlike trees. The definitions of starlike tree and double starlike tree are given and we proved that there exist no two cospectral non-isomorphic symmetric double starlike trees. URI: http://hdl.handle.net/123456789/1879 Files in this item: 1
dokdis.pdf ( 713.4Kb ) -
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 n-space ; 3. W-curves in Minkowski space-time; 4. Hyperbolic angle between vectors. In Chapter 1 the curves lying in hyperquadrics in Minkovski 3-space and Minkowski 4-space are studied. More precisely, the results related with the spacelike and timelike curves lying pseudosphere in Minkowski 3-space are presented. Also, the necessary and sufficient conditions for spacelike curves lying in pseudohyperbolic space in Minkowski 4-space are given. Curves of finite type 2 in Minkowski n-space are studied in details in Chapter 2. Also, there are given some known results related with finite type submanifolds. In Chapter 3, W-curves (i.e. the curves having constant all curvature functions) in Minkowski space-time are studied and some relations between W-curves 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 non-null vectors. The notion of hyperbolic angle between two timelike vectors is well-known, 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 non-null principal normal and all timelike curves of constant precession in Minkowski 3-space 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 ) -
Pavlović, Mirjana (Kragujevac, Serbia , 2011)[more][less]
Abstract: Dissertation is written in 60 pages and is divided into next parts: 1) Preface (pages 2-7) 2) Introduction (pages 8-29) 3) Concentration polynomial in low degrees (pages 30-56) 4) References (pages 57-60) which is consisted of 52 items Chapter 2 is divided into 9, and chapter 3 into 2 sections. In preface a short historical review of polynomials and their importance and position in mathematics are given. Especially interesting parts in preface are about number of zeros of polynomials in different sections of complex plane. In section 2.1 there are well known characteristic of Möbijus’ transformation which will be used further in dissertation. Section 2.2 of same chapter is consisted of relations of different norms which are being introduced to vector spaces of all polynomials with complex coefficients. In section 2.3 Hurwitz polynomials are explained. This class of polynomials which was being examined at the end of 19th century has found its real position in subject which is being examined in this dissertation. Jensen's formula (which also appeared at the end of 19th century) is described in section 4 from more aspects. In sections 5, 6, 7 and 8 the relation among Jensen's formula, Hardy's spaces of p degree, generalized Jensen's formula and Mahler's measure is given. In section 9 in dissertation the story about lower and upper boundaries of Jensen's functional is given (definition, motivation, some well known results and some new results of the author). The chapter 3 is consisted of results of the author which are related to lower boundaries of Jensen's functional for polynomials which satisfy the condition (1.2) of dissertation. In that case extreme functions are being determined. The main purpose of author is making intervals [-2k,-2k log 2] whose ends presents asymptotically lower and upper boundary of best lower boundary of Jensen's functional determined. The part of those results is published in "Computers and Mathematics with Applications". URI: http://hdl.handle.net/123456789/1913 Files in this item: 1
doktorska_disertacija(cirilica).pdf ( 476.9Kb ) -
Krtinić, Djordje (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]