Browsing Mathematics by Title
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Jovanović, Mirko (Beograd , 2016)[more][less]
Abstract: This dissertation is the contribution to the Metric fixed point theory, the area that has recently been rapidly developing. It contains five chapters. The first chapter gives the proof of one already known lemma. This lemma is used in the proof of Banach’s theorem for orbital complete metric spaces. The second chapter contains the proofs of eight theorems, which generalize some known results from the theory of fixed points in metric spaces (Boyd-Wong’s, ´ Ciri´c ’ s, Pant’ s, and other). Some of these theorems are modifications of the known ones, while three are completely new. Three theorems are proven in the third chapter. They generalize the result of fixed point of mapping defined in compact metric space given by Nemytzki, as well as one generalization of Edelstein’s theorem. The proofs and stated corollaries of some theorems are original. Chapter four discusses b-metric spaces as a generalization of metric spaces. The generalization of Zamfirescu’s theorem of b-metric spaces is presented as well as some of its applications. A new result concerning weakly almost contractive mappings is also determined. Chapter five contains some new results in cone metric spaces. Two theorems are presented as the analogue of the same theorems in the setting of standard metric spaces. A completely new theorem is established which results in the Banach’s theorem in cone metric spaces whereby the cone does not need to be normal. A generalization of Fisher’s theorem in cone metric spaces over a regular cone is also proven. Almost all results in this dissertation are confirmed by corresponding examples, which explain how these results differ from the already known results. URI: http://hdl.handle.net/123456789/4458 Files in this item: 1
Mirko_Jovanovic_dr.pdf ( 1.375Mb ) -
Jotić, Nikola (Belgrade , 1981)[more][less]
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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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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 ) -
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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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 ) -
Lazarević, Ilija (Belgrade)[more][less]