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Jovanović, Miljana (Beograd , 2024)[more][less]
Abstract: One of the main objectives of the Gaia mission of the European Space Agency is to construct a celestial reference frame at the wavelengths of the optical domain, Gaia CRF. This frame needs a link to the International Celestial Reference Frame – ICRF which is fixed with respect to distant objects (quasars). The objects serving for the purpose of linking are required to be visible in both domains (optical and radio). A set of 47 such objects has been proposed and included which in the radio domain have no detected extended emission. The mentioned objects are active galactic nuclei (AGN) the brightness of which varies over the whole electromagnetic spectrum. The brightness change may be due to activity in different AGN regions, but also to external factors. Such variations can lead to changes in the photocentre position and, consequently, to changes of the object coordinates. In order to establish which objects are suitable for linking these two frames we have examined the brightness variation in the optical domain. The objects have been observed from 2013 in the V and R bands. We have analysed the brightness, colour (V − R) and optical spectral index (α). It has been established that for the majority of objects the brightness is variable, or possibly variable. Almost 15% of all objects have significant changes in their brightness (more than 1 mag), only ∼10% are stable with minor brightness changes of ∼0.3 mag. The results concerning the change analysis of the colour and α are also presented. Based on these results 17 objects are chosen as suitable for linking ICRF to Gaia CRF. The results of the analysis, as well as the observed values, are essential for the examination of these objects because of their importance in astrometry, also in astrophysics. These data are relevant to a better understanding of formation and evolution of galaxies. URI: http://hdl.handle.net/123456789/5748 Files in this item: 1
MiljanaJovanovic-teza.pdf ( 6.418Mb ) -
Lukić, Žikica (Beograd , 2024)[more][less]
Abstract: The main goal of this dissertation is twofold. In the first part, two novel two- sample tests for matrix data are presented. The theoretical properties of these novel tests are investigated in the context of testing orthogonal invariance in distribution, while the empirical values are presented in other cases. The tests are not distribution-free under H0. Therefore, their quality is investigated through a power study by implementing the warp-speed bootstrap algorithm. The novel tests are applied to multiple cases of real data, primarily originating in the field of finance. These tests are the first of their kind for two-sample tests of positive definite symmetric matrix distributions and are based on Laplace and Hankel transforms. The second part of this dissertation addresses problems related to data segmentation (or change point detection). Two novel classes of univariate tests for offline data segmentation are outlined, and their theoretical properties are studied. The powers are estimated using the permutation bootstrap algorithm, and the novel tests are shown to have higher test powers than the well-known tests based on the characteristic function. The location of the change point is estimated, and the novel tests are empirically demonstrated to possess greater precision. These tests are applied to two distinct datasets from meteorology and macroeconomics, further emphasizing their applicability in real-case scenarios. Moreover, the two-sample test based on the Hankel transform is modified to address change point problems. The asymptotic properties of this novel test are derived. A power study is presented, demonstrating the quality of the novel test in small-sample scenarios. The novel test is applied to financial data, emphasizing the practical applicability of this approach. This represents the first test for change point inference based on integral transforms for matrix data. URI: http://hdl.handle.net/123456789/5747 Files in this item: 1
lukic_Zikica_Disertacija_com2.pdf ( 1.909Mb ) -
Todić, Bojana (Beograd , 2024)[more][less]
Abstract: This dissertation deals with the coupon collector problem, which in its simplest (classical) form can be formulated as follows: A collector wants to collect a set of n distinct coupons, by buying a single coupon each day. The random variable of interest is the waiting time until the collection is completed. The goal of the dissertation is to propose and analyze three new generalizations of the classical coupon collector problem obtained by introducing additional coupons with special purposes into the set of n standard coupons. The first two chapters are devoted to the results on the classical coupon collector problem and the known generalizations obtained by introducing additional coupons into the coupon set ([1], [2], [39], [54]). New results are presented in chapters 3,4, and 5. The third chapter of the dissertation is dedicated to the case where, in addition to the standard coupons, the coupon set consists of a null coupon (which can be drawn, but does not belong to any collection), and an additional universal coupon, that can replace any standard coupon. For the case of equal probabilities of standard coupons, the asymptotic behavior (as n → ∞) of the expectated value and variance of the waiting time for a fixed size subcollection of a collection of coupons is obtained when one or both probabilities of additional coupons are fixed, and the remaining coupons have equal small probabilities. These results, published in [27], generalize part of the results in [2]. The same problem is analyzed using a Markov chain approach, which led to the determination of the fundamental matrix and some related features of the collection process (probability that the coupon collection process ends in a certin way). These results are contained in the paper [24]. For the case of unequal probabilities of standard coupons, a class of bounds is derived for the first and second moments of the waiting time until the end of the experiment by using majorization techniques and refining the bounds proposed in [51]. The quality of the proposed bounds is tested in numerical experiments, and the specific bounds from the class with the most desirable properties are given. These results are published in [26]. The fourth chapter of the dissertation deals with the generalization in which the additional coupon (so called, penalty coupon) interferes with the collection of standard coupons in the sense that the collection process ends when the absolute difference between the number of collected standard coupons and the number of collected penalty coupons is equal to n. This generalization can be seen as a special case of the random walk with two absorbing barriers. The distribution and a simple upper bound on the first moment of the corresponding waiting time are determined by combinatorial considerations. The application of the Markov chain approach led to obtaining the fundamental matrix. These results are published in [53]. In the fifth chapter of the dissertation another additional coupon (so called reset coupon) is introduced, which acts as a reset button, in the sense that the set of coupons drawn up to time (day) t becomes empty if the reset coupon is drawn on day t+1. In the case of unequal probabilities of standard coupons, the distribution of the corresponding waiting time is obtained by combinatorial considerations. For the case of equal probabilities of obtaining standard coupons, For the case of equal probabilities, applying the first step analysis for the correspondingly constructed Markov chains led to the expressions for the expected waiting time and its simple form in terms of the beta function. These results are used for analysing the asymptotic behavior (when the size of the collection tends to infinity) of the expected waiting time, taking into account possible values of the probability of obtaining a reset coupon. These results are published in [25]. Setting the probabilities of the additional coupons to zero, all three generalizations of the coupon collector problem defined and analyzed in this dissertation as well as the obtained results reduce to the corresponding results for the classical coupon collector problem. URI: http://hdl.handle.net/123456789/5677 Files in this item: 1
Todic_Bojana_disertacija.pdf ( 1.004Mb ) -
Vicanović, Jelena (Beograd , 2024)[more][less]
Abstract: A convex continuous-time maximization problem is formulated and the nec- essary optimality conditions in the infinite-dimensional case are obtained. As a main tool for obtaining optimal conditions in this dissertation we use the new theorem of the alternative. Since there’s no a differentiability assumption, we perform a linearization of the problem using subdifferentials. It is proved that the multiplier with the objective function won’t be equal to zero. It was also shown that if the linear and non-linear constraints are separated, with additional assumptions it can be guaranteed that the multiplier with non-linear constraints will also be non-zero. In the following, an integral constraint is added to the original convex problem, so that a Lyapunov-type problem, i.e. an isoperimetric problem, is considered. Lin- earization of the problem using subdifferentials proved to be a practical way to ignore the lack of differentiability, so the optimality conditions were derived in a similar way. It is shown that the obtained results will also be valid for the vector case of the isoperimetric problem. Additionally, the optimality conditions for the smooth problem were considered. On the minimization problem, it was shown that the necessary conditions of Karush-Kuhn-Tucker type will be valid with the additional regularity constraint condition. Also, any point that satisfies the mentioned optimality conditions will be a global minimum. URI: http://hdl.handle.net/123456789/5676 Files in this item: 1
J.Vicanovic_doktorska_disertacija.pdf ( 2.198Mb ) -
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 )