Mathematical Sciences
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Rašković, Danilo (Naučna knjiga , 1965)[more][less]
URI: http://hdl.handle.net/123456789/4754 Dateien zu dieser Ressource: 1
Teorija_oscilacija_D_Raskovic_ocr.pdf ( 57.88Mb ) -
Tsirvoulis, Georgios (Beograd , 2019)[more][less]
Zusammenfassung: Asteroid families are populations of asteroids in the Main Belt that share a common origin, that is they are the fragments of energetic collisions between two asteroids. Their study over the years has produced a number of important results concerning the collisional and dynamical evolution of the Main Belt, the physical properties of the primordial bodies of the Solar System and the physics of energetic collisions, to name a few. The contribution of the present thesis can be summarized into two main topics: The first is the discovery of a new mechanism that leads to significant perturbations on the orbits of asteroids, and consequently on the evolution of asteroid families affected by it, and the second is the discovery of a couple of new families, each with its own peculiarities. The first part of this thesis was initially motivated by the irregular shape of the (1726) Hoffmeister asteroid family. In an effort to explain this peculiarity we carried out a thorough dynamical analysis of its past evolution and found out that none of the mechanisms known to affect the orbits of asteroids could explain it. Investigating further we discovered that the linear nodal secular resonance with the most massive asteroid (1) Ceres, is the mechanism responsible for the anisotropic inclination distribution of Hoffmeister family members. Having established the importance of the nodal secular resonance with Ceres, we sought to expand on the subject with the study of all linear secular resonances, nodal and periapsidal, involving not only (1) Ceres, but (4) Vesta, the second most massive asteroid, as well. To do so we utilized numerical integrations of test particles across the whole Main Belt, and evaluated the impact of these resonances on their orbits. Furthermore we identified all asteroid families crossed by one or more of these resonances. Two of these cases, the families of (1251) Seinajoki and (1128) Astrid were then studied in more detail, confirming the importance of the previously ignored secular resonances with massive asteroids. The second part details the discovery of two new asteroid families. The first one, that of (326) Tamara family, was motivated by the unexpectedly high number of dark asteroids in the Phocaea region, a part of the inner Main Belt which is expected to consist mostly of bright ones. Using all available physical data we were able to show that most of the dark asteroids therein belong to a single dynamical family, which we then further analyzed finding that it is 264 ± 43 Myrs old and that it could have a significant contribution to the influx of small dark asteroids toward the Near Earth region. The second discovered family, that of (633) Zelima, is a small cluster, sub-family of the large (221) Eos family. After identifying its members, we derived the age of the Zelima family, which turned out to be only about 3.66 Myrs. URI: http://hdl.handle.net/123456789/4752 Dateien zu dieser Ressource: 1
Tsirvoulis_Georgios.pdf ( 76.51Mb ) -
Jurković, Monika (Beograd , 2018)[more][less]
Zusammenfassung: The sub ject of this PhD thesis are Typ e I I Cepheids. Typ e I I Cepheids are pulsating Population I I stars with masses of around 0.5 0.6 M ⊙ . Their mass determines where they are p ositioned on the Hertzsprung-Russell diagram (HRD), that is, their luminosity and e ective temp erature. These stars can b e found in the Milky Way, the Magellanic Clouds, and in other distant galaxies. They o ccupy a narrow strip on the HRD which is called the instability strip. Here the radii and luminosity change p erio dically, and this change can b e seen in the light curves. Because of their age, and their p osition on the HRD, these variables form a separate p erio d-luminosity relation ( P L relation). Using the sp ectral energy distribution mo dels we determined in this thesis the e ective temp eratures and luminosities, and from evolutionary mo dels the masses and radii, for Typ e I I Cepheids and anomalous Cepheids in the Large and Small Magellanic Clouds. In the thesis, the rst p erio d- luminosity relation was constructed using b olometric magnitude ( M b ol ). The thesis also presents the reclassi cation of Typ e I I Cepheids from the Milky Way using the Fourier decomp osition of the light curves measured in V lter. The Fourier decomp osition was used to calculate the Fourier parameters, which were then used to compare the stars from the Milky Way with the sample of known Typ e I I Cepheids and anomalous Cepheids from the OGLE-I I I catalogue for the Large Magellanic Cloud. From the 59 stars (taken from the General Catalogue of Variable Stars), 18 turned out to b e anomalous Cepheids, 1 anomalous Cepheid pulsating in the rst overtone, 11 classical Cepheids, 2 p eculiar W Virginis stars or classical Cepheids, and 7 were found not to b e pulsating stars at all. URI: http://hdl.handle.net/123456789/4751 Dateien zu dieser Ressource: 1
Jurkovic_Monika.dok.dis.pdf ( 15.79Mb ) -
Stančić, Olivera (Beograd , 2018)[more][less]
Zusammenfassung: Hub Location Problems (HLP) represent an important class of optimiza- tion problems due to their numerous applications in many areas of real life. They often arise from practical situations that require routing of the flow from origin node (supplier) to the destination node (customer) under given conditions, such that the value of considered objective function is optimal. Hubs are special objects (nodes in the network) that represent centres for consolidation and flow collection between two selected locations - suppliers and customers. As transportation costs (per unit of flow) along the links that connect hub nodes are lower compared to other links in the network, directing the flow to hubs may lead to significant reductions of transportation cost in the network. The subject of this doctoral dissertation is one class of hub location problems, denoted as Hub Maximal Covering Problems (HMCPs) in the literature. The goal of HMCPs is to determine optimal locations for establishing certain number of hubs in order to maximize the total flow between all the covered origin-destination pairs, under the assumption of binary or partial covering. Three variants of the hub maximal covering problem are considered: uncapacitated single allocation p -hub maximal covering problem (USApHMCP), uncapacitated multiple allocation p -hub maximal covering problem (UMApHMCP) and uncapacitated r -allocation p -hub maximal covering problem (UrApHMCP). Note that the UrApHMCP has not been studied in the literature so far. All three considered problems are proven to be NP- hard. In case of USApHMCP, for the given set of hubs, the obtained sub-problem of optimal allocation of non-hub nodes by established hubs is also NP-hard. In this dissertation, new mathematical models for USApHMCP with binary and partial covering are proposed. The main advantage of the newly proposed models, in respect to existing ones from the literature, is the fact that small modifications of the new models enable their transformation to new models for p -hub maximal covering problems with different allocation schemes. More precisely, new models for UMApHMCP and UrApHMCP can be obtained from the newly proposed mod- els for USApHMCP in both coverage cases. All proposed models for USApHMCP and UMApHMCP are compared with the existing ones from the literature in the terms of efficiency within the framework of exact CPLEX 12.6 solver. Several hub data sets from the literature are used in numerical experiments when comparing the formulations. The obtained experimental results indicate that new models for UMApHMCP with both binary and partial coverage show the best performance in terms of solutions’ quality and execution times. For UrApHMCP and both coverage criteria, three mathematical models are proposed, and compared in terms of effi- ciency using the exact CPLEX 12.6 solver. It turns out that the exact solver finds optimal or feasible solutions only for small-size problem instances. Having in mind the complexity of all three problems under consideration and the results obtained by CPLEX 12.6 solver, the conclusion is that, in practice, exact methods can not provide solutions for large problem dimensions. For this reason, it was necessary to implement adequate heuristic or metaheuristic methods, in order to obtain high-quality solutions in short execution times, even in the case of large problem dimensions. Up to now, only simple but insufficiently effective heuris- tic methods for solving USApHMCP and UMApHMCP with binary coverage have been proposed in the literature, while the HMCP variants with partial coverage have not been previosly solved by using metaheuristic methods. As UrApHMCP with binary and partial coverage has not been previously considered in the litera- ture, no solution methods suggested for this problem existed up to now. Inspired by previous successful applications of variable neighborhood search method (VNS) to other hub location problems from the literature, this metaheuristic approach is applied to the considered HMCP problems. In this dissertation, several variants of VNS metaheuristic are designed and implemented: General Variable Neighborhood Search (GVNS) for USApHMCP, Basic Variable Neighborhood Search (BVNS) for UMApHMCP and a variant of General Variable Neighborhood Search (GVNS-R) for UrApHMCP. In the case of UrApHMCP, two additional metaheuristic meth- ods are proposed: Greedy Randomized Adaptive Search Procedure with Variable Neighborhood Descent (GRASP-VND) and Genetic Algorithm (GA). Constructive components of all proposed metaheuristics are adapted to the characteristics of the considered problems. Experimental study was conducted on the existing hub data sets from the lit- erature, which include instances with up to 1000 nodes in the network. The ob- tained results show that the proposed metaheuristics for the considered problems reach all known optimal solutions previously obtained by CPLEX 12.6 solver or establish new best-known solutions in significantly shorter CPU time compared to CPLEX 12.6. The proposed GVNS and BVNS metaheuristics quickly reach all known optimal solutions on small-size problem instances when solving USApHMCP and UMApHMCP, respectively. In the case of large-size problem instances, which have not been previously used for testing purposes for these problems, the proposed GVNS and BVNS return their best solutions in short execution times. The results obtained by the proposed GVNS-R and GRASP-VND for UrApHMCP on large-size problem instances indicate their effectiveness in both coverage cases. The proposed GA method showed to be successful only for UrApHMCP in binary covering, on instances up to 200 nodes. The variants of hub maximal covering problems considered in this dissertation are important from both theoretical and practical points of view. The new mathe- matical models proposed in this dissertation for the considered variants of HMCP, represent a scientific contribution to the theory of hub location problems, mathemat- ical modeling and optimization. Designed and implemented metaheuristic methods for solving the studied variants of HMCP are the scientific contribution to the field of optimization methods for solving location problems, as well as the development of software. The considered variants of HMCP have numerous applications in the optimization of telecommunication and transport systems, air passenger and goods transport, emergency services, postal and other delivery systems, so that the results obtained in this doctoral dissertation can be applied in practice, partially or com- pletely. URI: http://hdl.handle.net/123456789/4750 Dateien zu dieser Ressource: 1
StancicOliveradisertacija.pdf ( 1.688Mb ) -
Melentijević, Petar (Beograd , 2018)[more][less]
Zusammenfassung: In this thesis we study sharp estimates of gradients and operator norm estimates in harmonic function theory. First, we obtain Schwarz-type inequalities for holomorphic mappings from the unit ball B n to the unit ball B m , and then analoguous inequalities for holomorphic functions on the disk D without zeros and pluriharmonic functions from the unit ball B n to ( − 1 , 1) . These extend results from [ 32 ] and [ 18 ]. Also, we give a new proof of the fact that positive harmonic function in the upper-half plane is a contraction with resprect to hyperbolic metrics on both H and R + ([ 47 ]). Besides that, in the second chapter, we construct the examples to show that the analoguous does not hold for the higher-dimensional upper-half spaces. All mentioned results are from the authors’ paper [55]. In the third chapter we intend to calculate the exact seminorm of the weighted Berezin transform considered as an operator from L ∞ ( B n ) to the ”smooth” Bloch space ([57]). The fourth chapter contains results concerning Bergman projection. We solve the problem posed by Kalaj and Marković in [ 28 ] on determining the exact seminorm of the Bergman projections from L ∞ ( B n ) to the B ( B n ) . The crucial obstacle is the fact that B ( B n ) is equipped with M− invariant gradient seminorm. Also, we provide the sharp gradient estimates of the Bergman projection of an L p function in the unit ball B n , as well as its consequences on Cauchy projection and certain gradient estimates for the functions from the Hardy and Bergman spaces.We obtain the exact values of the Bloch’s seminorms and norms for the Cauchy projection on L ∞ ( S n ) . These results are based on the papers [56] and [58]. The last chapter contains the proof of the one part of Hollenbeck-Verbitsky conjecture from [ 26 ]. Exactly, we find the exact norms of ( | P + | s + | P − | s ) 1 s for 0 < s ≤ 2 on L p ( T ) , where P + is the Riesz projection and P − = I − P + . Also we give the appropriate dual estimates and prove that they are sharp. The paper [ 45 ] is motivated by the results from [25] and [33]. URI: http://hdl.handle.net/123456789/4749 Dateien zu dieser Ressource: 1
doktorat_Petar_merged.pdf ( 1.507Mb )