Browsing Doctoral Dissertations by Title
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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]
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Vujanović, Božidar (None)[more][less]
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Rusov, Lazar (Belgrade , 1964)[more][less]
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Ivanović, Miloš (Kragujevac, Srbija , 2010)[more][less]
URI: http://hdl.handle.net/123456789/1838 Files in this item: 1
mivanovic-disertacija-pun-tekst.pdf ( 11.57Mb ) -
Pejović, Nadežda (Belgrade)[more][less]
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Perović, Miodrag (Belgrade)[more][less]
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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]
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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 rst-order auto-regressive 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 non-random 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 two-dimensional 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 two-dimensional component-wise 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 rst-order auto-regressive 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]
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Ašković, Radomir (Beograd , 1966)[more][less]
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Ašković, Radomir (Belgrade , 1966)[more][less]
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Roslavcev, Maja (Beograd , 2021)[more][less]
Abstract: n this thesis we deal with the existence of Gröbner bases for finitely generated ide- als in rings of polynomials over some classes of rings which are not Noetherian. The theory of Gröbner bases is highly developed when we observe the ring of polynomials over a field or over a Noetherian ring. The case when the base ring is non-Noetherian is less examined. In that sense, the rings which will be of interest here are valuation rings of Krull dimension zero, valuation domains of Krull dimension one, also the generalization of the last: Prüfer domains of Krull dimension one. Von Neumann regular commutative rings and (p − 1)-nil-clean commutative rings will also be a matter of discussion. The conclusions of the thesis can be applied to Bezout and Boolean rings, as these form the subclasses of Prüfer and von Neumann regular rings, respectively. The thesis is mostly focused on rings of polynomials with one indeterminate. URI: http://hdl.handle.net/123456789/5245 Files in this item: 1
MRoslavcev_TEZA.pdf ( 3.044Mb ) -
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 well-known 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 well-known 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 cup-length of some manifolds of this type. URI: http://hdl.handle.net/123456789/4298 Files in this item: 1
phdRadovanovic_Marko.pdf ( 1.476Mb ) -
Bokan, Neda (Belgrade)[more][less]
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Knežević, Miljan (Beograd , 2014)[more][less]
Abstract: This thesis considers various properties of Euclidean harmonic mappings, quasiconformal mappings and generalized harmonic mappings, which are harmonic with respect to the conformal metric on the image surface. In particular, we obtained the answers to many questions concerning these classes of functions and that are related to the determination of different properties that are of essential importance for validity of the results such as those that generalize famous inequalities of the Schwarz-Pick type. The approach used was geometrical in nature, via analyzing the properties of the Gaussian curvature of the conformal metrics we are dealing with. URI: http://hdl.handle.net/123456789/4280 Files in this item: 1
phdKNEZEVIC_MILJAN.pdf ( 1.312Mb ) -
Kostić, Petar (b , 2023)[more][less]
Abstract: The models of radio synchrotron emission of supernova remnants (SNRs) imply uniform density ahead of shock wave, so the evolution of luminosity is usu- ally studied in such an environment, most often through the surface-brightness-to- diameter dependence, the Σ–D relation. This field aims to better understand the SNR evolution, the emission models, but also the methods for determining their distance. It is not an easy task because of a very large scatter in the Σ–D Milky Way sample. The dissertation puts a different perspective at the Σ–D relation (usually treated as power-law function), assuming that non-uniform environment around the stars considerably affects its shape and slope, that may vary during the SNR expansion. It makes the ambient density structure an important factor whose impact must be investigated. The numerical code for hydrodynamic (HD) simulations and the emission model were developed. The 3D HD simulations were performed in different non-uniform environments, including low-density bubbles and a variety of clumpy models. Based on the simulation results, a semi-analytical 3D spherically-symmetric model of HD and Σ–D evolution of SNRs in clumpy medium was developed, which is used to generate large Σ–D samples. The results show that after entering the clumpy medium the SNR brightness enhances, but afterward the Σ–D slope steepens, shortening the brightness evolu- tion lifetime. Despite the evident increase in slope in clumpy medium, the Galactic sample average slope flattens at ≈ 13–50 pc. After analyzing the generated SNR samples in clumpy medium it is concluded that the significant flattening and scatter in Galactic sample originates in sporadic emission jumps of individual SNRs in a limited diameter interval. The additional analyses of selection effects are needed to investigate these issues. URI: http://hdl.handle.net/123456789/5606 Files in this item: 1
Kostic_Petar_disertacija.pdf ( 1.947Mb ) -
Vrećica, Siniša (Belgrade , 1984)[more][less]
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Grujić, Vladimir (Belgrade)[more][less]