Browsing Mathematics by Title

Karapandžić, Đorđe (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/142 Files in this item: 1
phdDjordjeKarapandzic.pdf ( 3.246Mb ) 
Doder, Dragan (Beograd , 2011)[more][less]

Andrejić, Vladica (Beograd , 2010)[more][less]
Abstract: U ovom radu posmatramo princip dualnosti (i jake dualnosti) za Osermanove mnogostrukosti i uopxtavamo ga za pseudoRimanov sluqaj. Osnovni ci je dokazati princip dualnosti za Osermanove mnogostrukosti u opxtem sluqaju ili konstrukcija eventualnih kon traprimera. Za sada smo u sta u da damo samo rezultate pod speci fiqnim dodatnim uslovima. Prva mogu nost je mali indeks pseudo Rimanove mnogostrukosti, gde dokazujemo da jaka dualnost va i za Rimanove i Lorencove prostore. Druga mogu nost su prostori malih dimenzija gde dokazujemo da jaka dualnost va i kad dimenzija nije ve a od qetiri. Posled a olakxavaju a okolnost sa kojom radimo tiqe se malog broja sopstvenih vrednosti redukovanog Jakobijevog operatora, gde posmatramo dvolisnoOsermanove tenzore krivine. U tom sluqaju radimo sa jakim uslovima iz definicije kvazispecijalnih Osermanovih tenzora krivine i elimo da doka emo da pod ima va i princip dualnosti. Konaqan rezultat je da skorospecijalan Oser manov tenzor krivine mora biti specijalan Osermanov. U nastavku postav amo obratan problem, te pokuxavamo da istra imo pod kojim uslovima algebarski tenzor krivine za koji va i princip dualnosti mora biti Osermanov. Potvrdan rezultat dobili smo u dimenziji tri, kao i u sluqaju kada se Fidlerova suma sastoji od samo jednog qlana. URI: http://hdl.handle.net/123456789/2479 Files in this item: 1
phdAndrejicVladica.pdf ( 513.6Kb ) 
Dajović, Slobodan (Belgrade)[more][less]

Đorđević, Radosav (Kragujevac , 1991)[more][less]
Abstract: The thesis consists of six chapters. Chapter 1 contains the structures, in which the probability logics are realized, and the basic methods of nonstandard analysis which are used in the other chapters. In Chapter 2 the syntax and semantics of the following probability logics are presented: the logic with the probability quantifiers L_Ap, the logic with the integral operators L_A_∫ , the logic with the operator of conditional expectation L_AE and adapted probability logic L_ad. Moreover, the certain important results about these logics are given. The problems of Barwise’s completeness, completeness, compactness, the existence of analytic and hyperfinite models for biprobability logics LA_P1_P2, LA_∫_1_∫_2 and L_ad in absolute continuous and singular cases are solved in Chapter 3. The manyprobability logic BC{L_AP_i:i∊I}, I∊A obtained by Boolean combinations of probability logics L_AP is introduced and some modeltheoretical properties of that logic are given in Chapter 4. In Chapter 5 the probability logic L^2AP∀ of second order is introduced, which is motivated by Keisler’ s problems with L_AP∀ and some topological logics. The problem of completeness for the logic L^2AP∀ is proved. In Chapter 6 cylinder probability algebras are introduced and some possibilities to solve problems for these algebras (which are characteristics of standard cylinder algebras, as the representation, axiomatization and decidability) are presented. URI: http://hdl.handle.net/123456789/189 Files in this item: 1
phdRadosavSDjordjevic.pdf ( 2.407Mb ) 
Djerasimović, Božidar (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/140 Files in this item: 1
phdBozidarPDjerasimovic.pdf ( 2.343Mb ) 
Stančić, Olivera (Beograd , 2018)[more][less]
Abstract: 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 origindestination 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 subproblem of optimal allocation of nonhub nodes by established hubs is also NPhard. 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 smallsize 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 highquality 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 (GVNSR) for UrApHMCP. In the case of UrApHMCP, two additional metaheuristic meth ods are proposed: Greedy Randomized Adaptive Search Procedure with Variable Neighborhood Descent (GRASPVND) 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 bestknown solutions in significantly shorter CPU time compared to CPLEX 12.6. The proposed GVNS and BVNS metaheuristics quickly reach all known optimal solutions on smallsize problem instances when solving USApHMCP and UMApHMCP, respectively. In the case of largesize 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 GVNSR and GRASPVND for UrApHMCP on largesize 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 Files in this item: 1
StancicOliveradisertacija.pdf ( 1.688Mb ) 
Stojanović, Stevan (Belgrade , 1969)[more][less]

Berisha, Muharrem (Pristina , 1979)[more][less]

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

Melentijević, Petar (Beograd , 2018)[more][less]
Abstract: In this thesis we study sharp estimates of gradients and operator norm estimates in harmonic function theory. First, we obtain Schwarztype 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 upperhalf 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 higherdimensional upperhalf 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 HollenbeckVerbitsky 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 Files in this item: 1
doktorat_Petar_merged.pdf ( 1.507Mb ) 
Popović, Biljana (Belgrade)[more][less]

Stanimirović, Predrag (Niš)[more][less]
URI: http://hdl.handle.net/123456789/190 Files in this item: 1
phdPredragStanimirovic.pdf ( 5.471Mb ) 
Dotlić, Milan (Beograd , 2015)[more][less]
Abstract: The thesis considers numerical methods for the computation of subsurface flow and transport of mass and energy in an anisotropic piecewise continuous medium. This kind of problems arises in hidrology, petroleum engineering, ecology and other fields. Subsurface flow in a saturated medium is described by a linear partial differential equation, while in an unsaturated medium it is described by the Richards nonlinear partial differential equation. Transport of mass and energy is described by advectiondiffusion equations. The thesis considers several finite volume methods for the discretization of diffusive and advective terms. An interpolation method for discretization of diffusion through discontinuous media is presented. This method is applicable to several nonlinear finite volume schemes. The presence of a well in the reservoir determines the subsurface flow to a large extent. Standard numerical methods produce a completely wrong flux and an inaccurate hydraulic head distribution in the well viscinity. Two methods for the well flux correction are introduced in this thesis. One of these methods gives secondorder accuracy for the hydraulic head and firstorder accuracy for the flux. Explicit and implicit time discretizations are presented. Preservation of the maximum and minimum principles in all considered schemes is analyzed. All considered schemes are tested using numerical examples that confirm teoretical results. URI: http://hdl.handle.net/123456789/4236 Files in this item: 1
phdDotlic_Milan.pdf ( 5.137Mb ) 
Georgijević, Dušan (Belgrade)[more][less]

Miličić, Pavle (Belgrade)[more][less]

Trifunović, Miodrag (Novi Sad)[more][less]

Vuković, Veljko (Pristina , 1984)[more][less]

Mostafa, Attila (Beograd , 2015)[more][less]
Abstract: First of all I would like to express my praises and sincere thanks to almighty Allah, start with no end and end will never start, for his divine assistance and guidance, which gave me the ability to succeed. I Thank you Allah, for life, health, and the energy that you have given me to reach my professional goals. Iwould like to gratefully and sincerely thank my supervisor Prof PhD Miodrag Mateljevi´c as well as dr Miljan Kneževi´c for their guidance, understanding, patience, and most importantly, their friendship during my graduate studies at my faculty. Their mentorship was paramount in providing a wellrounded experience consistent my career goals. My sincere appreciation, thanks and gratitude to all the academic staff members of Faculty of Mathematics, University of Belgrade. I would to thank Libyan Embassy in Belgrade to provide material and moral support. URI: http://hdl.handle.net/123456789/4339 Files in this item: 1
Attia Mostafa_thesis.pdf ( 3.337Mb ) 
Louka, Hana Almoner (Beograd , 2016)[more][less]
Abstract: This thesis has been written under the supervision of my mentor dr. Vladimir Bo zin at the University of Belgrade in the academic year 2016. The topic of this thesis is quantum information theory, with special attention to quantum contract signing protocols. The thesis is divided into four chapters. Chapter 1 gives introduction to Quantum mechanics and necessary mathematical background. Chapter 2 is about quantum information theory. Quantum algorithms, including Schor's and Grover's, are described. Chapter 3 deals with classical contract signing, and cryptography. Also discussed is the RSA algorithm and BB84 quantum key distribution. Chapter 4 describes quantum signing protocol, and proves, among other things, asymptotic behavior for probability of cheating. URI: http://hdl.handle.net/123456789/4342 Files in this item: 1
hanathesis21.pdf ( 711.2Kb )