Browsing Doctoral Dissertations by Title
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Krapež, Aleksandar (Belgrade , 1980)[more][less]
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Obradović, Milutin (Belgrade , 1984)[more][less]
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Radičić, Biljana (Beograd , 2016)[more][less]
Abstract: In thisdissertation, k-circulantmatricesareconsidered,where k is an arbitrary complexnumber.Themethodforobtainingtheinverseofanon- singular k-circulantmatrix,foranarbitrary k ̸= 0, ispresented,andusing that method,theinverseofanonsingular k-circulantmatrixwithgeometric sequence (witharithmeticsequence)isobtained,foranarbitrary k ̸= 0 (for k = 1). Usingthefullrankfactorizationofàmatrix,theMoore-Penrosein- verseofasingular k-circulantmatrixwithgeometricsequence(witharithme- tic sequence)isdetermined,foranarbitrary k (for k = 1). Foranarbitrary k, the eigenvalues,thedeterminantandtheEuclideannormofa k-circulantma- trix withgeometricsequencei.e.witharithmeticsequencearederived,and boundsforthespectralnormofa k-circulantmatrixwithgeometricsequence are determined.Also, k-circulantmatriceswiththe rstrow (F1; F2; :::;Fn) i.e. (L1;L2; :::;Ln), where Fn i.e. Ln is the nth Fibonaccinumberi.e.Lucas number,areinvestigatedandtheeigenvaluesandtheEuclideannormsof suchmatricesareobtained.BoundsforthespectralnormsoftheHadamard inversesoftheabovematrices,foranarbitrary k ̸= 0, arealsodetermined. Attheendofthisdissertation,theeigenvalues,thedeterminantandbounds for thespectralnormofa k-circulantmatrixwithbinomialcoe cientsare derived,andboundsforthespectralnormoftheHadamardinverseofsuch matrix, foranarbitrary k ̸= 0, aredetermined. URI: http://hdl.handle.net/123456789/4456 Files in this item: 1
Disertacija_Biljana_Radicic.pdf ( 1.609Mb ) -
Milić, Svetozar (Belgrade)[more][less]
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Zdravković, Momčilo (Belgrade , 1965)[more][less]
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Stojković, Vojislav (Belgrade , 1981)[more][less]
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Krgović, Dragica (Belgrade , 1982)[more][less]
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Bogdanović, Stojan (Novi Sad)[more][less]
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Janjić, Slobodanka (Belgrade , 1985)[more][less]
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Shkodra, Sadri (Priština)[more][less]
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Jovanović, Aleksandar (Beograd)[more][less]
Abstract: The dissertation consists of five chapters. The Chapters 1 and 2 contain the known results from the model theory and the set theory which are used in the other chapters. A classification of the properties of filters is given in Chapter 3. Some connections between combinatoric properties are made and the theorems about existence are also given. Ultraproducts are studied in Chapter 4. The structure of ultraproducts is connected with the structure of ultrafilters and cardinality of ultraproducts. Moreover, some other problems are studied, as the 2- cardinality problem. In the case of a measurable cardinal the connection with continuum problem is presented and several theorems of the cardinality of ultraproducts are proved. The problems about the real measure are studied in Chapter 5. The forcing is presented and by using results from Chapter 3 and Chapter 4 several properties are proved. The notion of norm of measure is introduced and some possible relations between additivity and norm of a measure are studied. Real large measurable cardinals are introduced analogously as the other large cardinals. The inspiration for this introduction were Solovay’s results of equconsistency of the theory ZDF + ”there is a measurable cardinal” and the theory ZDF+”there is a real measurable cardinal”. The relative consistency of the real large measurable cardinals with respect to ZDF+”the corresponding large cardinal” is proved by a generalization of Solovay’s forcing. URI: http://hdl.handle.net/123456789/683 Files in this item: 1
work001AleksandarJovanovic.pdf ( 16.02Mb ) -
Jovanov, Đurica (Beograd , 1991)[more][less]
URI: http://hdl.handle.net/123456789/4128 Files in this item: 1
Varijacione_nejednacine.PDF ( 910.5Kb ) -
Angelov, Trajče (Belgrade , 1980)[more][less]
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Janković, Vladimir (Belgrade , 1983)[more][less]
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Simić, Slavko (Belgrade , 1997)[more][less]
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Lukić, Mirko (Belgrade)[more][less]
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Kulenović, Mustafa (Sarajevo)[more][less]
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Radojčić, Nina (Beograd , 2018)[more][less]
Abstract: In this dissertation, three NP-hard optimization problems are studied and va- rious computational intelligence methods are considered for solving them, with a special emphasis on the possibilities of applying fuzzy logic in order to improve the performances of proposed methods. In addition, it is shown how fuzzy logic can be incorporated into a model to make it more adequate to real world applications. The first problem considered is the Risk-Constrained Cash-in-Transit Vehicle Routing Problem (RCTVRP) that represents a special case of the vehicle routing problem (VRP). Similar to the classical VRP, the aim is to determine the collection routes from one depot to a number of customers in order to minimize the overall travel distance (or cost). Additionally, the safety aspect of the routed risk constraints are introduced in the case of RCTVRP. The RCTVRP concerns the issue of secu- rity during the transportation of cash or valuable goods (e.g. in the cash-in-transit industry). The other two problems studied in this dissertation belong to the class of loca- tion problems: the Load Balancing Problem (LOBA) and the Max-Min Diversity Problem (MMDP). The goal of the LOBA problem is to locate a fixed number of facilities, such that the difference between the maximum and minimum number of customers served by each facility is balanced. The LOBA model is useful in cases where customers naturally choose the closest facility. The MMDP consists of se- lecting a subset of a fixed number of elements from a given set in such a way that the diversity among the selected elements is maximized. This problem also arises in real world situations encompassing a variety of fields, particularly the social and biological sciences. In order to solve the RCTVRP, a fuzzy GRASP (Greedy Randomized Adaptive Search Procedure) is hybridized with Path Reliking (PR) methodology. Carefully adjusted fuzzy modification incorporated into the proposed GRASP for the RC- TVRP improved its performance. Moreover, in this dissertation a new PR structure is implemented and can be used for other vehicle routing problems. To improve the algorithm’s time complexity, a new data structure for the RCTVRP is incor- porated. The proposed fuzzy GRASP with PR hybrid shows better computational performance compared to its non-fuzzy version. Furthermore, computational results on publicly available data sets indicate that the proposed algorithm outperforms all existing methods from the literature for solving the RCTVRP. For solving the LOBA problem two efficient hybrid metaheuristic methods are proposed: a combination of reduced and standard variable neighborhood search met- hods (RVNS-VNS) and hybridization of evolutionary algorithm and VNS approach (EA-VNS). The proposed hybrid methods are first benchmarked and compared to all the other methods on existing test instances for the LOBA problem with up to 100 customers and potential suppliers. In order to test the effectiveness of the pro- posed methods, we modify several large-scale instances from the literature with up to 402 customers and potential suppliers. Exhaustive computational experiments show that the proposed hybrid methods quickly reach all known optimal solutions while providing solutions on large-scale problem instances in short CPU times. Re- garding solution quality and running times, we conclude that the proposed EA-VNS approach outperforms other considered methods for solving the LOBA problem. EA approach is also proposed for solving the MMDP. Computational experi- ments on a smaller benchmark data set showed that the classic EA quickly reached all optimal solutions obtained previously by an exact solver. However, some of the larger instances of MMDP were challenging for classic EA. Although researchers have established the most commonly used parameter setting for EA that has good performance for most of the problems, it is still challenging to choose the adequate values for the parameters of the algorithm. One approach to overcome this is chan- ging parameter values during the algorithm run. As part of this dissertation this problem was addressed by extending the evolutionary algorithm by adding a fuzzy rule formulated from EA experts’ knowledge and experience. The implemented fuzzy rule changes the mutation parameter during the algorithm run. The results on tested instances indicate that the proposed fuzzy approach is more suitable for solving the MMDP than classic EA. For all three problems addressed whereas the smaller instances that CPLEX was able to solve, obtained optimal solutions were used for comparison with proposed methods and all of the proposed methods obtained these optimal solutions. Moreover, in this dissertation it has been shown that fuzzy logic is a successful tool in modeling the RCTVRP. In this problem the risk constraints are set by using a risk threshold T on each route and thus, the routes with risk larger than T are forbidden. However, in this dissertation the aim is to take into account the probability of being robbed along each route instead of just allowing solutions with routes that satisfy the risk constraints. A new fuzzy model for the RCTVRP is developed which takes into account the value of the risk index of each route and the solutions with lower values of risk indexes on their routes are considered superior. In order to achieve that fuzzy numbers are used in the improved model. Moreover, two mixed integer program formulations of new fuzzy model are developed and presented in this dissertation. The introduced fuzzy model is compared with the model from the literature using an adequate example and the advantages of the newly proposed fuzzy RCTVRP is demonstrated. Computational experiments are performed and the comparison of the two models given in the paper show that the newly presented approach leads to safer routes. URI: http://hdl.handle.net/123456789/4737 Files in this item: 1
tezaNinaRadojicic.pdf ( 1.665Mb ) -
Popstanojević, Zoran (Belgrade , 1963)[more][less]
URI: http://hdl.handle.net/123456789/224 Files in this item: 1
phdZoranPopstojanovic.pdf ( 1.549Mb ) -
Muzika Dizdarević, Manuela (Beograd , 2017)[more][less]
Abstract: Subject of this doctoral thesis is the application of algebraic techniques on one of the central topics of combinatorics and discrete geometry - polyomino tiling. Polyomino tilings are interesting not only to mathematicians, but also to physicists and biologists, and they can also be applied in computer science. In this thesis we put some emphasis on possibility to solve special class of tiling problems, that are invariant under the action of nite group, by using theory of Gr obner basis for polynomial rings with integer coe cients. Method used here is re ecting deep connection between algebra, geometry and combinatorics. Original scienti c contribution of this doctoral thesis is, at the rst place, in developing a techniques which enable us to consider not only ordinary Z?tiling problems in a lattice but the problems of tilings which are invariant under some subgroups of the symmetry group of the given lattice. Besides, it provides additional generalizations, originally provided by famous mathematicians J. Conway and J. Lagarias, about tiling of the triangular region in hexagonal lattice. Here is a summary of the content of the theses. In the rst chapter we give an exposition of the Gr obner basis theory. Especially, we emphasize Gr obner basis for polynomial rings with integer coe cients. This is because, in this thesis, we use algorithms for determining Gr obner basis for polynomials with integer coe cients. Second chapter provides basic facts about regular lattices in the plane. Also, this chapter provides some fundamental terms of polyomino tiling in the square and hexagonal lattice. Third chapter of this thesis is about studying Ztilings in the square lattice, which are invariant under the subgroup G of the group of all isometric transformations of the lattice which is generated by the central symmetry. One of the steps to resolve this problem was to determine a ring of invariants PG and its generators and relations among them. We use Gr obner basis theory to achieve this. Forth chapter covers the analysis of Ztilings in the hexagonal lattice which are symmetric with respect to the rotation of the plane for the angle of 120 . Main result of the fourth chapter is the theorem which gives conditions for symmetric tiling of the triangular region in plane TN, where N is the number of hexagons on each side of triangle. This theorem is one of the possible generalizations of the well known result, provided by Conway and Langarias. Fifth chapter provides another generalization of Conway and Lagarias result, but this time it is about determining conditions of tiling of triangular region TN in the hexagonal lattice not only with tribones, but with nbones. nbone is basic shape of of n connected cells in the hexagonal lattice, where n is arbitrary integer. URI: http://hdl.handle.net/123456789/4503 Files in this item: 1
muzikadizarevic.manuela.pdf ( 33.23Mb )