Browsing Mathematics by Title
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Stamatović, Biljana (Beograd , 1999)[more][less]
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Jelić, Milena (Belgrade)[more][less]
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Milovanović - Aranđelović, Marina (Beograd , 2016)[more][less]
Abstract: The aim of this dissertation is to present new properties of some classes of contractive mappings, and applications of this results to nonlinear analysis. It contain six chapters. The first chapter gives basic properties of semi-metric spaces. New result is extension of Borel - Lebesque theorem to semi metric spaces. The second chapter contain generalization of Niemytzki’s fixed point theorem. In third chapter the notion of measure of non-compactness are extended to class of semimetric spaces. New fixed point theorem for condensing mappings defined on semi-metric spaces is presented. Further three chapters contains new common fixed points theorems of Mair - Keeler type, new results for accretive mappings and new common fixed point results for mappings defined on probabilistic metric spaces. URI: http://hdl.handle.net/123456789/4482 Files in this item: 1
DisertacijaMilovanovic-Arandjelovic_Marina.pdf ( 1.599Mb ) -
Živković, Miodrag (Belgrade , 1990)[more][less]
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Ivanović, Lav (Belgrade , 1983)[more][less]
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Bulatović, Ranislav (Belgrade , 1983)[more][less]
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Đuranović-Miličić, Nada (Belgrade , 1980)[more][less]
URI: http://hdl.handle.net/123456789/69 Files in this item: 1
phdNadaDjuranovicMilicic.pdf ( 3.214Mb ) -
Žižović, Mališa (Belgrade , 1980)[more][less]
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Rečkovski, Nikola (Skopje , 1978)[more][less]
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Graovac, Jelena (Univerzitet u Beogradu , 2014)[more][less]
Abstract: U svetu u kome ˇzivimo, internet i digitalni zapis uˇcinili su da ogromne koliˇcine sirovih podataka postanu dostupne ˇsirokoj javnosti. Jedan ameriˇcki menadˇzer je joˇs davno izjavio: "Raˇcunari su nam obe´cali fontanu mudrosti, a ovo ˇsto smo dobili je poplava podataka" [20]. Sirovi podaci, neadekvatno strukturirani i razliˇcitih formata, sadrˇzaja i kvaliteta su retko od koristi. Neophodno ih je pripremiti, analizirati i na osnovu toga do´ci do informacija i znanja koja na taj naˇcin stiˇcu neprocenjivu vrednost. Istraˇzivanje podataka (eng. data mining) je interdisciplinarno polje infor- matike koje se bavi automatskim ili polu-automatskim otkrivanjem znanja u podacima. Njegov osnovni zadatak je netrivijalna ekstrakcija informa- cija iz podataka, i to informacija koje su implicitne, prethodno nepoznate i potencijalno korisne. Koriste se metode koje su u preseku veˇstaˇcke in- teligencije, maˇsinskog uˇcenja, statistike i sistema baza podataka [97]. Zadaci koji se reˇsavaju u okviru Istraˇzivanja podataka mogu biti prediktivni (klasi- fikacija, regresija, analiza vremenskih serija) ili deskriptivni (klasterovanje, sumarizacija, pravila pridruˇzivanja, analiza redosleda, otkrivanje anomalija). U okviru ove doktorske disertacije bavimo se problemom klasifikacije tek- stova na osnovu njihovog sadrˇzaja. Smatra se da je preko 80% dostupnih informacija saˇcuvano u tekstualnom obliku. Ve´cina informacija je zapisana prirodnim jezikom, odnosno jezikom koji koriste ljudi za svakodnevnu ko- munikaciju. Za oˇcekivati je da ´ce tehnologije automatske obrade podataka zapisanih prirodnim jezikom postati vode´ce u svetu. Glavni doprinos di- sertacije ogleda se u predstavljanju novih metoda za klasifikaciju tekstual- nih dokumenata. Prva metoda predstavlja unapredenje metode razvijene u cilju otkrivanja autorstva teksta [38]. Metoda je zasnovana na predstavlja- nju dokumenta kao profila koji sadrˇzi fiksiran broj n-grama bajtova koji se pojavljuju u dokumentu, i meri razliˇcitosti pomo´cu koje se odreduje klasa kojoj dokument pripada. Ova metoda je jeziˇcki nezavisna i ne zahteva nikakvu prethodnu obradu teksta niti predznanje o sadrˇzaju teksta ili jeziku na kome je tekst napisan. Druga metoda se zasniva na odabranim koncep- tima kao predstavnicima klasa koji se dobijaju iz srpskog wordnet-a, leksiˇcko semantiˇcke mreˇze za srpski jezik. Deo rezultata iz ove disertacije je sadrˇzan u radovima [23, 27, 22, 21, 56, 26, 25, 24] koji su objavljeni, predati za ob- javljivanje ili su u fazi pripreme. Disertacija je organizovana na slede´ci naˇcin. U glavi 1 je prikazan uvod u oblast klasifikacije podataka, u okviru koga su prikazane vrste klasifikacije, procena kvaliteta klasifikacije i primeri primene. Poseban osvrt dat je na klasifikaciju tekstualnih dokumenata. Prikazani su razliˇciti naˇcini predstavljanja dokumenata kao jednog od najvaˇznijiih koraka u procesu klasifikacije. Predoˇceni su i mnogi problemi i izazovi koji se javlja- ju. Prikazani su korpusi klasifikovanih tekstova na srpskom, engleskom, ki- neskom i arapskom jeziku koji ´ce biti koriˇs´ceni u daljem istraˇzivanju. Uvodna glava zavrˇsava se jednim filozofskim pogledom na proces klasifikacije. Glava 2 daje pregled postoje´cih leksiˇckih resursa za srpski jezik [17] koji se razvijaju u okviru Grupe za jeziˇcke tehnologije na Matematiˇckom fakul- tetu Univeziteta u Beogradu. Ideja je da se ukljuˇcivanjem morfoloˇskih, sin- taksiˇckih i semantiˇckih informacija sadrˇzanih u resursima unapredi proces klasifikacije tekstova na srpkom jeziku, kao jednom od morfoloˇski bogatijih jezika. Predstavljeni su korpusi srpskog jezika, elektronski reˇcnik i srpski wordnet kao i raznovrsne tehnologije koje se koriste za njihovu obradu a koje se razvijaju u okviru Grupe. U glavi 3 su prikazane postoje´ce metode maˇsinskog uˇcenja koje su do sada imale veoma uspeˇsnu primenu u procesu klasifikacije. Prikazane su metode zasnovane na drvetima odluˇcivanja, metode zasnovane na pravilima i rastojanju, statistiˇcki zasnovane metode, metode zasnovane na neuronskim mreˇzama i metode zasnovane na podrˇzavaju´cim vektorima. Nove metode za klasifikaciju teksta prikazane su u glavi 4. U okviru prve metode zasnovane na n-gramima bajtova, uvedeni su nova mera razliˇcitosti i novi teˇzinski faktori u odnosu na osnovnu varijantu metode. Teˇzinski faktori su dodeljeni n-gramima u okviru profila klasa, reflektuju´ci znaˇcaj koji n-grami imaju za pripadaju´cu klasu. Smatra se da n-grami koji imaju ve´cu frekvenciju a pripadaju manjem broju klasa imaju ve´ci znaˇcaj za klasu kojoj pripadaju. Uvodenje ovih teˇzinskih faktora rezultovalo je modifikacijom metode na dva naˇcina: modifikacija na nivou mere razliˇcitosti i modifikacija na nivou profila klase. Druga metoda se odnosi na koriˇs´cenje informacija sadrˇzanih u srpskom wordnetu i srpskom elektronskom reˇcniku u cilju klasifikacije teksta na srp- skom jeziku. Ova metoda zasniva se na pridruˇzivanju odabranih koncepata iz srpskog wordnet-a klasama, na osnovu kojih se izraˇcunava mera pripadnosti klasi i vrˇsi pridruˇzivanje dokumenta nekoj od klasa. Rezultati prikazanih novih metoda sumirani su u okviru glave 5. Na srp- skom korpusu je prikazano poredenje prve metode i njenih modifikacija zas- novanih na n-gramima bajtova, karaktera i reˇci. Osnovna varijanta metode i njene modifikacije za n-grame bajtova, testirani su na korpusima na srpskom, engleskom, kineskom i arapskom jeziku, ˇcime je demonstrirana jeziˇcka neza- visnost metode. U okviru Priloga 1 dodatno su predstavljeni svi rezultati dobijeni testiranjem metode za razliˇcite vrednosti parametara, za sve pred- stavljene mere razliˇcitosti, na svim pomenutim korpusima. Druga metoda testirana je samo na korpusu na srpskom jeziku. Poredenje prikazanih rezultata sa drugim rezultataima iz ove oblasti dato je u glavi 6 a glava 7 prikazuje zakljuˇcke i pravce daljeg rada. URI: http://hdl.handle.net/123456789/3746 Files in this item: 1
PhD_JelenaGraovac.pdf ( 3.870Mb ) -
Janić, Milan (Novi Sad , 1982)[more][less]
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Vojvodić, Gradimir (Belgrade)[more][less]
Abstract: Results from model theory of mixed-valued predicate calculus are presented, by using results of the model theory of classical predicate calculus. The thesis consists of four chapters. The basic notions, definitions and properties are given in the introductory chapter. The main theorems, which are proved in Chapter 1, are the following: the weak separable theorem for k-models (the characteristic theorem for mixed-valued predicate calculus with respect to other logics based of Post's algebras); the theorem about the connection between k-models of mixed-valued predicate calculus and models of classical predicate calculus; and the theorem of the difference between the theory of k-models of mixed-valued predicate calculus and theory of models of classical predicate calculus. By using results from the previous chapter, the theorems of mixed-valued predicate calculus (which analogous to the well-known theorems from classical predicate calculus: Craig’s interpolation lemma, Beth’s theorem about definability and the II_ε-theorem) are proved in Chapter 2. Results concerning structures of mixed-valued equivalence relations and congruence relations (which is connected with the well-known results from universal algebras about the structure of equivalence relations and congruence relations) are presented in Chapter 3. URI: http://hdl.handle.net/123456789/329 Files in this item: 1
phdGradimirVojvodic.pdf ( 1.565Mb ) -
Šami, Zoran (Belgrade)[more][less]
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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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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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Krapež, Aleksandar (Belgrade , 1980)[more][less]