Browsing Mathematics by Title

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]

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 ) 
Minčić, Svetislav (Novi Sad)[more][less]

Lopandić, Dragomir (Belgrade)[more][less]

Udovičić, Enes (Belgrade , 1980)[more][less]

Stanimirović, Zorica (Belgrade , 2007)[more][less]
Abstract: U ovom radu opisani su različiti genetski algoritmi (GA) za rešavanje četiri NPteška hab lokacijska problema: problem phab medijane neograničenih kapaciteta sa jednostrukim alokacijama (USApHMP), problem phab 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 phab 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 NPhard hub location problems are described: Uncapacitated Single Allocation phub Center Problem (USApHCP), Capacitated Single Allocation phub 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 phub 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 wellknown 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 largescaled 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 ) 
Šukilović, Tijana (Beograd , 2015)[more][less]
Abstract: In the present work we classify left invariant metrics of arbitrary signature on fourdimensional nilpotent Lie groups. Their geometry is extensively studied with special emphasis on holonomy groups and decomposability of metrics. Also, isometry groups are completely described and we give examples of metrics where strict inequalities Isplit < Iaut < I hold. It is interesting that Walker metrics appear as the underlying structure of neutral signature metrics on the nilpotent Lie groups with degenerate center. We nd necessary and su cient condition for them to locally admit nilpotent group of isometries. Finally, we solve the problem of projectively equivalent metric on fourdimensional nilpotent Lie groups by showing that left invariant metric is either geometrically rigid or have projectively equivalent metrics that are also a nely equivalent. All a nely equivalent metrics are left invariant, while their signature may change. URI: http://hdl.handle.net/123456789/4453 Files in this item: 1
Doktorska_disertacija__Tijana_Sukilovic.pdf ( 1.501Mb ) 
Đorić, Mirjana (Beograd , 1994)[more][less]
Abstract: It is an interesting problem to study the geometry of Riemannian manifolds by investigating the propetries of geometric objects on them. It turns out that the features of the geometry of a family of geometric objects on a Riemannian manifold strongly influence the geometry of the ambient space. In this paper we focus on the same kind of problems considering the extrinsic and intrinsic geometry of tubes about geodesics on Kahler and Sasakian manifolds. In order to obtain our results we mainly work with Jacobi vector fields because this falls among the best ways of analysing the geometry of normal and tubular neighborhoods. In Chapter II we compute the explicit formulas for the shape operator of tubes about cogeodesics on Sasakian space forms, using the technique of Jacobi vector fields. Further, in Chapter III we characterize locally Hermitian symmetric spaces and complex space forms considering the shape operator and the Ricci operator of tubes about geodesics on Kahler manifolds. Finally, in Chapter IV we characterize Sasakian space forms and locally cosymmetric spaces by analysing the action of the shape operator and the Ricci operator on tubes about cpgeodesics on Sa URI: http://hdl.handle.net/123456789/4091 Files in this item: 1
Geometrija_geodezijskih.PDF ( 1.664Mb ) 
Pavlović, Miroslav (Belgrade , 1983)[more][less]

Dimitrijević, Ivan (Beograd , 2017)[more][less]
Abstract: Einstein theory of gravity successfully describes the Solar system. It also predicts the existence of the black holes, gravitational lenses and gravitational waves, which have been observed successfully. On the other hand Einstein theory of gravity is not tested on the large cosmic sccale. Therefore, we consider the nonlocal modi ed gravity and get new solutions for the cosmic scale factor a(t). Moreover we consider spacetime perturbations of the de Sitter space. URI: http://hdl.handle.net/123456789/4500 Files in this item: 1
doktorska_disertacija_Dimitrijevic_Ivan.pdf ( 1.342Mb ) 
Grujić, Jelena (Beograd , 2015)[more][less]
Abstract: Despite its theoretical beauty and many phenomenological evidences, general relativity is not a complete theory and should be modi ed. Namely, under rather general conditions, general relativity yields cosmological solutions with zero size of the universe at its beginning, what means an in nite matter density. In order to solve this problem we consider nonlocal modi cation of general relativity. In particular, we analyze two nonlocal models and present their nonsingular bounce cosmological solutions for the cosmic scale factor. URI: http://hdl.handle.net/123456789/4314 Files in this item: 1
Grujic_Jelena.pdf ( 1.783Mb ) 
Rašajski, Borivoje (None)[more][less]

Vujanović, Božidar (None)[more][less]

Perović, Miodrag (Belgrade)[more][less]

Miloradović, Slobodan (Belgrade , 1982)[more][less]
URI: http://hdl.handle.net/123456789/87 Files in this item: 1
phdSlobodanMiloradovic.pdf ( 1.641Mb ) 
Pavićević, Žarko (Belgrade , 1983)[more][less]

Glavaš, Lenka (Beograd , 2015)[more][less]
Abstract: The subject of this doctoral dissertation is related to the problems of extreme values in strictly stationary random sequences. It belongs to the topical area of probability and statistics, broadly applicable to real life situations and in many scienti c elds. It relies on large number of seminal articles and monographs. The main aim of the dissertation is to determine the asymptotic behavior of maxima of some incomplete samples from the rstorder autoregressive processes with uniform marginal distributions. The dissertation consists of three chapters. New results (the theoretical ones and the results of computer simulations) are presented in the third chapter. Two types of the uniform ARp1q process pXnqnPN are considered: positively correlated and negatively correlated process, with the lag one correlation p1q : CorrpXn 1;Xnq equal to 1 r and 1 r , respectively, where r ¥ 2 is the parameter of the underlying process. Let pcnqnPN be a nonrandom 0 1 sequence, such that lim nÑ8 1 n n ¸j 1 cj p P r0; 1s. This sequence of degenerate random variables is introduced with the purpose to correspond to the sequence pXnq in the following sense: r.v. Xj is observed if cj 1, otherwise r.v. Xj is not observed (missing observation). Let us use the notation: the r.v. Mn : max 1¤j¤n Xj is maximum of the complete (size n) sample from the random sequence pXnq, and the r.v. Mn is what is called partial maximum, i.e. the maximal element of incomplete sample tXj : cj 1; 1 ¤ j ¤ nu. Based on di erent, speci c deterministic sequences pcnq it is proved that the limiting distribution, as n Ñ 8, of the twodimensional random vector Mn;Mn , is not uniquely determined by the limit value p. This appears as a consequence of the fact that for the uniform ARp1q process one of the weak dependence conditions does not apply. Namely, the uniform ARp1q process does not satisfy the local condition under which clustering of extremes is restricted. As a consequence of this property, some interesting conclusions about asymptotic joint distributions of random variables Mn and Mn are reached. In the cases when the partial maximum Mn is determined by an arbitrary point process there are presented results obtained by simulations. The rst two chapters are rather informative. Having in mind interest in studying the asymptotic behavior of linearly standardized twodimensional componentwise maxima the role of the rst chapter is to anticipate the concept of multivariate extreme values. In the second chapter the basic terms in the time series analysis are formulated, with the accent on the linear stationary models, especially on rstorder autoregressive models. The special attention is dedicated to the uniform ARp1q processes, their properties and existing results concerning their extremal behavior. Still open questions are mentioned in the conclusion, in the very end of the third chapter. URI: http://hdl.handle.net/123456789/4454 Files in this item: 1
Doktorska_disertacija_Lenka_Glavas.pdf ( 1.195Mb ) 
Despotović, Radivoje (Novi Sad , 1983)[more][less]

Radovanović, Marko (Beograd , 2015)[more][less]
Abstract: By Borel's description, integral and mod 2 cohomology of ag manifolds is a polynomial algebra modulo a wellknown ideal. In this doctoral dissertation, Gr obner bases for these ideals are obtained in the case of complex and real Grassmann manifolds, and real ag manifolds F(1; : : : ; 1; 2; : : : ; 2; k; n). In the case of Grassmann manifolds, Gr obner bases are applied in the study of Z cohomology of complex Grassmann manifolds. It is wellknown that, besides Borel's description, this cohomology can be characterized in terms of Schubert classes. By establishing a connection between this description and Gr obner bases that we obtained, a new recurrence formula that can be used for calculating (all) Kostka numbers is derived. Using the same method for the small quantum cohomology of Grassmann manifolds (instead of the classical), these formulas are improved. In the case of real ag manifolds F(1; : : : ; 1; 2; : : : ; 2; k; n), Gr obner bases are used to obtain new results on the immersions and embeddings of these manifolds, and for the calculation of the cuplength of some manifolds of this type. URI: http://hdl.handle.net/123456789/4298 Files in this item: 1
phdRadovanovic_Marko.pdf ( 1.476Mb )