Browsing Doctoral Dissertations by Title
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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 ) -
Petrović, Miroslav (Belgrade , 1983)[more][less]
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Vesković, Miroslav (Belgrade , 1987)[more][less]
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Dugošija, Đorđe (Belgrade)[more][less]
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Prešić, Slaviša (Belgrade)[more][less]
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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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Gligorić, Milan (Belgrade , 1973)[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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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 )