Browsing Doctoral Dissertations by Title

Levajković, Tijana (Novi Sad , 2011)[more][less]
Abstract: In this dissertation we study the main properties of the operators of Malliavin calculus de ned on a set of singular generalized stochastic processes, which admit chaos expansion representation form in terms of orthogonal polynomial basis and having values in a certain weighted space of stochastic distributions in white noise framework. In the rst part of the dissertation we focus on white noise spaces and introduce the fractional Poissonian white noise space. All four types of white noise spaces obtained (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian) can be identi ed through unitary mappings. As a contribution to the Malliavin di erential theory, theorems which characterize the operators of Malliavin calculus, extended from the space of square integrable random variables to the space of generalized stochastic processes were obtained. Moreover the connections with the corresponding fractional versions of these operators are emphasized and proved. Several examples of stochastic di erential equations involving the operators of the Malliavin calculus, solved by use of the chaos expansion method, have found place in the last part of the dissertation. Particularly, obtained results are applied to solving a generalized eigenvalue problem with the Malliavin derivative and a stochastic Dirichlet problem with a perturbation term driven by the OrnsteinUhlenbeck operator. URI: http://hdl.handle.net/123456789/3824 Files in this item: 1
DR_Tijana.pdf ( 1.518Mb ) 
Anokić, Ana (Beograd , 2017)[more][less]
Abstract: Optimization problems arise from many reallife situations. The development of adequate mathematical models of optimization problems and appropriate solution methods are of great importance for performance of real systems. The subject of this doctoral dissertation is a novel vehicle scheduling problem (VSP) that arises from optimizing the transport of agricultural raw materials. The organization of transport of raw materials is of great importance in the initial phase of production. This is particularly evident in the case of agricultural raw materials, because their price in the market is very low, and therefore, the costs of their transport represent the largest part of the total production cost. For this reason, any reduction of time and money spent in this early production stage directly increases the company’s profitability. The considered variant of VSP arises from optimizing the transport of sugar beet in a factory for sugar production in Serbia, but it can also be applied in a wider context, i.e., to optimize the transport of raw materials or goods in large companies under the same or similar conditions. The considered problem involves a number of specific constraints that distinguish it from existing variants of the vehicle scheduling problem. Therefore, mathematical models proposed in the literature for other variants of VSP do not describe adequately the considered problem. The complexity of the newly introduced VSP is analyzed. It is proven that the introduced VSP belongs to the class of NPhard problems by comparing its relaxation with the Parallel Machine Scheduling Problem (PMSP). PMSP is known to be NPhard, as it is equivalent to the Partitioning problem. From the established analogy between the relaxation of the considered VSP and PMSP, it is concluded that the VSP introduced in this dissertation is NPhard. New mathematical models of the considered problem that involve all problem specific properties, are developed. The proposed mathematical models are compared in sense of efficiency by using Lingo 17 and CPLEX MIP 12.6.2 solvers. Experimental results showed that both exact solvers provided optimal or feasible solutions only for smallsize reallife problem instances. However, this was expectable, having in mind the NPhardness of the considered problem. Therefore, heuristic and metaheuristic method seem to be appropriate approaches for solving problem instances of larger dimension. Due to specific properties of the considered problem, the existing implementations of heuristic and metaheuristic methods for vehicle routing and scheduling problems can not be directly applied. For this reason, different variants of wellknown Variable Neighborhood Search (VNS) metaheuristic, as well as Greedy Randomized Adaptive Search Procedure (GRASP), are designed. The constructive elements of the proposed VNS and GRASP implementations are adapted to the characteristics of the considered vehicle scheduling problem. A subproblem of the proposed variant of vehicle scheduling problem, denoted as VSPP is considered first. VSPP is obtained from the initial VSP by excluding problem specific constraints regarding vehicle arriving times to each location and to the factory area. Two metaheuristic algorithms are designed as solution methods for this subproblem: Basic Variable Neighborhood Search  BVNS, and Greedy Randomized Adaptive Search Procedure  GRASP. Both proposed approaches were tested on instances based on reallife data and on the set of generated instances of lager dimensions. Experimental results show that BVNS and GRASP reached all optimal solutions obtained by exact solvers on smallsize reallife problem instances. On mediumsize reallife instances, BVNS reached or improved upper bounds obtained by CPLEX solver under time limit of 5 hours. BVNS showed to be superior compared to GRASP in the sense of solution quality on medium size reallife instances, as well as on generated largesize problem instances. However, general conclusion is that both proposed methods represent adequate solution approaches for the subproblem VSPP. BVNS provides solutions of better quality compared to GRASP, while GRASP outperforms BVNS regarding the average CPU time required to produce its best solutions. For the initial vehicle scheduling problem (VSP) that includes all problem specific constraints, three VNSbased metaheuristic methods are designed and implemented: Basic Variable Neighborhood Search  BVNS, Skewed Variable Neighborhood Search  SVNS, and Improved Basic Variable Neighborhood Search  BVNSi. BVNS and SVNS use the same neighborhood structures, but different search strategies in local search phase: BVNS uses Best improvement strategy, while SVNS uses First improvement strategy. All three VNSbased methods are tested on reallife and generated problem instances. As it was expected, experimental results showed that BVNS outperformed SVNS regarding solution quality, while SVNS running time was significantly shorter compared to BVNS. The third designed algorithm BVNSi represents a variant of BVNS that uses more general neighborhood structures compared to the ones used in BVNS and SVNS. The use of such neighborhood structures lead to the simplicity of BVNSi and shorter running times compared to BVNS. Two variants of BVNSi method that exploit different strategies in Local search phase are designed: BVNSiB with best improvement strategy and BVNSiF with First improvement strategy. The results of computational experiments for all proposed VNSbased methods for VSP are analyzed and compared. Regarding the quality of the obtained solutions, BVNS method shows the best performance, while SVNS needed the shortest average running times to produce its best solutions. Two variants of BVNSi method succeeded to find new best solutions on two medium size real life instances and to solve large size instances in shorter running time compared to BVNS and SVNS, respectively. However, both BVNSiB and BVNSiF turn out to be less stabile than BVNS and SVNS on reallife and generated inatances. In the case of one largesize generated instance, both BVNSi variants had significantly worse performance compared to BVNS and SVNS, which had negative impact on their average objective values and average running times. The proposed vehicle scheduling problem is of great practical importance for optimizing the transport of agricultural raw materials. It is planned to use the obtained results in practice (partially or completely), as a support to decision makers who organize transportation of in the early production phase. From the theoretical point of view, the developed mathematical models represent a scientific contribution to the fields of optimization and mathematical modeling. The variants of VNS methods that are developed and adapted to the problem, as well as comparison of their performances, represent a scientific contribution to the field of metaheuristic methods for solving NPhard optimization problems. URI: http://hdl.handle.net/123456789/4664 Files in this item: 1
Anokic_Ana_disertacija.pdf ( 2.688Mb ) 
Zejnullahu, Abdullah (Priština)[more][less]
URI: http://hdl.handle.net/123456789/136 Files in this item: 1
phdAbdullahZejnullahu.pdf ( 1.513Mb ) 
Kovač, Nataša (Beograd , 2018)[more][less]
Abstract: Dissertation title : Metaheuristic approach for solving one class of optimization problems in transp ort Abstract : Berth Allo cation Problem incorp orates some of the most imp ortant de cisions that have to b e made in order to achieve maximum e ciency in a p ort. Terminal manager of a p ort has to assign incoming vessels to the available b erths, where they will b e loaded/unloaded in such a way that some ob jective function is optimized. It is well known that even the simpler variants of Berth Allo cation Problem are NPhard, and thus, metaheuristic approaches are more convenient than exact metho ds, b ecause they provide high quality solutions in reasonable compu tational time. This study considers two variants of the Berth Allo cation Problem: Minimum Cost Hybrid Berth Allo cationProblem (MCHBAP) and Dynamic Mini mum Cost Hybrid Berth Allo cationProblem (DMCHBAP), b oth with xed handling times of vessels. Ob jective function to b e minimized consists of the following com p onents: costs of p ositioning, sp eeding up or waiting of vessels, and tardiness of completion for all vessels. Having in mind that the sp eed of nding highquality solutions is of crucial imp ortance for designing an e cient and reliable decision supp ort system in container terminal, metaheuristic metho ds represent the natural choice when dealing with MCHBAP and DMCHBAP. This study examines the fol lowing metaheuristic approaches for b oth typ es of a given problem: two variants of the Bee Colony Optimization (BCO), two variants of the Evolutionary Algorithm (EA), and four variants of Variable Neighb orho o d Search (VNS). All metaheuristics are evaluated and compared against each other and against exact metho ds inte grated in commercial CPLEX solver on reallife instances from the literature and randomly generated instances of higher dimensions. The analysis of the obtained results shows that on reallife instances all metaheuristics were able to nd optimal solutions in short execution times. Randomly generated instances were out of reach for exact solver due to time or memory limits, while metaheuristics easily provided highquality solutions in short CPU time in each run. The conducted computational analysis indicates that metaheuristics represent a promising approach for MCHBAP and similar problems in maritime transp ortation. The results presented in this pap er represent a contribution to the elds of combinatorial optimization, op erational research, metaheuristic metho ds, and b erth allo cation problem in the container terminals. URI: http://hdl.handle.net/123456789/4747 Files in this item: 1
N_Kovacdoktorska_disertacija.pdf ( 3.540Mb ) 
Putnik, Stanimir (Belgrade)[more][less]

Vrdoljak, Božo (Belgrade)[more][less]

Đurić, Milan (Belgrade , 1965)[more][less]

Ašković, Tomislav (Belgrade , 1976)[more][less]

Cijan, Boris (Belgrade)[more][less]

Čanak, Miloš (Belgrade)[more][less]

Hotomski, Petar (Belgrade , 1982)[more][less]

Rizvanolli, Fuat (Belgrade , 1982)[more][less]

Kordić, Stevan (Beograd , 2016)[more][less]
Abstract: Constrain satisfaction problems including the optimisation problems are among the most important problems of discrete mathematics with wide area of application in mathematics itself and in the applied mathematics. Dissertation study optimisation problem and presents an original method for finding its exact solution. The name of the method is Sedimentation Algorithm, which is introduced together with two heuristics. It belongs to the class of branchandbound algorithms, which uses backtracking and forward checking techniques. The Sedimentation Algorithm is proven to be totally correct. Ability of the Sedimentation Algorithm to solve different type of problems is demonstrated in dissertation by its application on the Boolean satisfiability problems, the Whitehead Minimisation Problem and the Berth Allocation Problem in container port. The best results are obtained for Berth Allocation Problem, because its modelling for Sedimentation Algorithm includes all available optimisation techniques of the method. The precise complexity estimation of the Sedimentation Algorithm for the Berth Allocation Problem is established. Experimental results verify that the Sedimentation Algorithm is capable to solve the Berth Allocation Problem on the state of art level. URI: http://hdl.handle.net/123456789/4413 Files in this item: 1
StevanKordic.pdf ( 2.477Mb ) 
Kapetanović, Miodrag (Belgrade)[more][less]

Cvetković, Predrag (Belgrade , 1976)[more][less]

Arbutina, Bojan (Faculty of Mathematics, University of Belgrade , 2009)[more][less]
Abstract: The main research topic of this dissertation are extreme mass ratio contact close binary systems, q 0.1, of W Ursae Majoris (W UMa) type. These close binaries (CBs) represent an interesting class of objects in which ”normal”, approximately one solar mass mainsequence star is in contact with a significantly less massive companion, M2 ∼ 0.1 M . Earlier theoretical investigations of these systems found that there is a minimum mass ratio qmin = M2/M1 ≈ 0.085 − 0.095 (obtained for n = 3 polytrope  fully radiative primary) above which these CBs are stable and could be observed. If the mass ratio is lower than qmin, or, equivalently, if orbital angular momentum is only about three times larger than the spin angular momentum of a massive primary, a tidal instability develops (Darwin’s instability) forcing eventually the stars to merge into a single, rapidly rotating object (such as FK Comtype stars or blue stragglers). However, there appear to be some W UMatype CBs with empirically obtained values for the mass ratio below the theoretical limit for stability. The aim of this dissertation is to try to resolve the discrepancy between theory and observations by considering rotating polytropes. By including in theory the effects of higher central condensation due to rotation we were able to reduce qmin to the new theoretical value qmin = 0.070 − 0.074, for the overcontact degree f = 0 − 1, which is more consistent with the observed population. Other candidate systems for stellar mergers such as AM CVntype stars have also been discussed in the dissertation. URI: http://hdl.handle.net/123456789/716 Files in this item: 1
phdBojanArbutina.pdf ( 6.326Mb ) 
Ćelić, Momir (Banjaluka , 1986)[more][less]

Pavlović, Marko (, 2017)[more][less]
Abstract: Supernova (SN) explosions disperse the different heavy elements across the Uni verse. These elements are the building blocks which make up the world around and inside us. Supernova remnants (SNRs) are extraordinary astronomical objects that are also of high scientific interest, because they provide insights into aforementioned supernova explosion mechanisms, and because they are important sources of Galac tic cosmic rays (CRs). Radio observations are among the oldest means to study these objects. The radio luminosity and spectra of SNRs, especially young ones, requires active acceleration of electrons by the SNR shocks. In this doctoral dissertation, radio evolution of SNRs is investigated by using threedimensional hydrodynamic modelling and nonlinear diffusive shock acceleration of CRs in SNRs. Hydrodynamic simulations, developed and adopted in this dissertation, allow us to explicitly account for the shock modification by CRs. We also include consistent numerical treatment of magnetic field amplification (MFA) due to CR resonant and nonresonant streaming instabilities. We modelled the peculiar nature of radio evo lution of the youngest known Galactic SNR G1.9+0.3 and concluded that increasing radio emission is a common occurrence among very young SNRs. Our model ena bled us to make important conclusions about the present and predictions about the future properties of radio emission from this SNR. We also developed more general model of the radio evolution of SNRs, by performing simulations for wide range of the relevant physical parameters, such as the ambient density, the supernova ex plosion energy, the acceleration efficiency and the MFA efficiency. We confirm the reliability of our radio evolutionary tracks on a observation sample consisting of Galactic and extragalactic SNRs. This dissertation also deals with one of the most important questions surroun ding our current understanding of the magnetic fields in SNRs. We conclude that equipartition is a justified assumption especially between the CR electrons and the magnetic fields in evolved SNRs, in the SedovTaylor phase of evolution. Our work also offers a possible explanation how can equipartition between CRs and magnetic field in the interstellar medium be achieved. Type of modeling, presented in this thesis, is expected to be a useful tool for fu ture observers working on powerful radio telescopes such as ALMA, MWA, ASKAP, SKA and FAST. Simulations should provide important information about the evolu tionary stage of the observed SNRs, as well as to characterize the physical conditions in the shocks where the relativistic particles are accelerated. Simulations could help us to predict the science output of future large scale surveys, as well as to explain new, often unexpected results obtained by observations. URI: http://hdl.handle.net/123456789/4759 Files in this item: 1
MPavlovic.pdf ( 14.32Mb ) 
Pavlović, Marko (Beograd , 2018)[more][less]
Abstract: Supernova (SN) explosions disperse the diﬀerent heavy elements across the Uni verse. These elements are the building blocks which make up the world around and inside us. Supernova remnants (SNRs) are extraordinary astronomical objects that are also of high scientiﬁc interest, because they provide insights into aforementioned supernova explosion mechanisms, and because they are important sources of Galac tic cosmic rays (CRs). Radio observations are among the oldest means to study these objects. The radio luminosity and spectra of SNRs, especially young ones, requires active acceleration of electrons by the SNR shocks. In this doctoral dissertation, radio evolution of SNRs is investigated by using threedimensional hydrodynamic modelling and nonlinear diﬀusive shock acceleration of CRs in SNRs. Hydrodynamic simulations, developed and adopted in this dissertation, allow us to explicitly account for the shock modiﬁcation by CRs. We also include consistent numerical treatment of magnetic ﬁeld ampliﬁcation (MFA) due to CR resonant and nonresonant streaming instabilities. We modelled the peculiar nature of radio evo lution of the youngest known Galactic SNR G1.9+0.3 and concluded that increasing radio emission is a common occurrence among very young SNRs. Our model ena bled us to make important conclusions about the present and predictions about the future properties of radio emission from this SNR. We also developed more general model of the radio evolution of SNRs, by performing simulations for wide range of the relevant physical parameters, such as the ambient density, the supernova ex plosion energy, the acceleration eﬃciency and the MFA eﬃciency. We conﬁrm the reliability of our radio evolutionary tracks on a observation sample consisting of Galactic and extragalactic SNRs. This dissertation also deals with one of the most important questions surroun ding our current understanding of the magnetic ﬁelds in SNRs. We conclude that equipartition is a justiﬁed assumption especially between the CR electrons and the magnetic ﬁelds in evolved SNRs, in the SedovTaylor phase of evolution. Our work also oﬀers a possible explanation how can equipartition between CRs and magnetic ﬁeld in the interstellar medium be achieved. Type of modeling, presented in this thesis, is expected to be a useful tool for fu ture observers working on powerful radio telescopes such as ALMA, MWA, ASKAP, SKA and FAST. Simulations should provide important information about the evolu tionary stage of the observed SNRs, as well as to characterize the physical conditions in the shocks where the relativistic particles are accelerated. Simulations could help us to predict the science output of future large scale surveys, as well as to explain new, often unexpected results obtained by observations. URI: http://hdl.handle.net/123456789/4736 Files in this item: 1
MPavlovic.pdf ( 14.32Mb ) 
Marković, Zoran (Pennsylvania)[more][less]
Abstract: The results from this thesis are obtained by using notions and procedures which are wellknown in Kripke structures in the first place, together with some other constructions. They might provides insights about intuitionistic formal theories analogous to insights about classical logic provided by results of classical model theory. The thesis consists of three chapters. The definitions concerning syntax of the first order intuitionistic logic, the definitions and theorems about Kripke structures, Hayting algebras and saturated theories are given in Chapter 1. In the first part of the next chapter a few results about the connection between forcing and classical satisfaction relation are proved. In the second part of that chapter three alternatives of the antecedent of the omitting type theorem are presented, and an omitting types theorem is proved. It is important that there are many applications of that theorem. In Chapter 3 the following two kinds of products are considered: prime products of saturated theories and ultra products and reduced products of Kripke structures. In the first part of that chapter the following property is proved: a simple analogue of ultraproduct construction can be defined in terms of saturated theories. The important result from the second part of Chapter 3 is that the class of formulas preserved under reduced products is much broader than the class of formulas which are intuitionistically equivalent to Horn formulas. URI: http://hdl.handle.net/123456789/317 Files in this item: 1
phdZoranMarkovic.pdf ( 9.114Mb )