Browsing Mathematics by Title

Stanojević, Vera (Belgrade , 1983)[more][less]

Šili, Endre (Belgrade , 1985)[more][less]

Petrović, Mihailo (Paris , 1894)[more][less]
URI: http://hdl.handle.net/123456789/3737 Files in this item: 1
Mik_Alas_Pariz_1894_high.pdf ( 23.25Mb ) 
Ababoub, Ali (Belgrade , 2013)[more][less]
Abstract: This thesis has been written under the supervision of my mentor Prof. Miodrag Mateljevi c, and my comentor dr. Vladimir Bo zin at the University of Belgrade in the academic year 20122013. The topic of this thesis is Complex analysis related with geometric function theory, more precisely the theory of quasiconformal mappings in the Euclidean ndimensional space. For good survey of the eld, see F. W. Gehring [20] in the handbook of K uhnau [33] which also contains many other surveys on quasiconformal mappings and related topics. The main source in this dissertation is J. V ais al a [67]. The thesis is divided into three chapters. Chapter 1 is divided into 5 sections. In this chapter, we focus on quasiconformal mappings in Rn and discuss various equivalent de nitions. We give The Modulus of family of curves in the rst section, geometric de nition of quasiconformal space mappings in second section, analytic de nition of quasiconformal space mappings in third section, equivalence of the de nitions in fourth section, and the Beltrami equation in fth section. Chapter 2 is divided into 5 sections. We begin by generalizing the class of Lip ( ), 0 < 1, and some properties of that class. Chapter 2 is devoted to understanding the properties by introducing the notion of Linearity, Di erentiability, and majorants. A majorant function is a certain generalization of the power functions t , this is done in the rst section. In the second section we introducing the notion of moduli of continuity with its Some Properties which gotten from I.M. Kolodiy, F. Hildebrand paper [39]. In third section we produced harmonic mapping as preliminary for the fourth section which including subharmonicity of jfjq of harmonic quasiregular mapping in space. In the last section we introducing estimation of the Poisson kernel which were extracted from Krantz paper [42]. Chapter 3 is divided into 3 sections. This chapter is include the main result in this dissertation. In this chapter we prove that !u( ) C!f ( ), where u : ! Rn is the harmonic extension of a continuous map f : @ ! Rn, if u is a Kquasiregular map and is bounded in Rn with C2 boundary. Here C is a constant depending only on n, !f and K and !h denotes the modulus of continuity of h. We also prove a version of this result for !extension domains with cuniformly perfect boundary and quasiconformal mappings, and we state some results regarding HQC self maps of the quadrant Q = fz : z = x + iy; x; y > 0g. URI: http://hdl.handle.net/123456789/3048 Files in this item: 1
Ali Ababaoub Li ... asicionformal Mappings.pdf ( 501.4Kb ) 
Dautović, Šejla (Beograd , 2022)[more][less]
Abstract: The goal of this dissertation is to develop logics with the aim of formalizing Bayesian confirmation theory. As such, the very topic of this dissertation is in the field of probabilistic logic. In Bayesian theory there are qualitative and quantitative concepts of confirmation. Ac cording to the first of these two terms, the event E probabilistically confirms the second event F if the conditional probability of the event F (with the condition E) is greater than unconditional probabilities. On the other hand, the quantitative approach studies the degree to which E confirms F , which is formalized by relevance measures of confirmation, binary functions with arguments E and F . Carnap used the notion of the degree of confirmation as the basic term for the formal apparatus of inductive logic. The main results of the dissertation are probabilistic logics with operators of confirma tion that correspond to existing measures of relevance from the literature, and theoretical predictions related to these logics, such as deduction and completeness theorems, as well as decision results. The importance of the development of such logical systems, except in the direct formalization of important Bayesian concepts, lies in their expressiveness: for each measure of relevance that will be logically formalized, the resulting logical language is rich enough to express many basic operators of probabilistic logic from the literature, which are the operators of standard probability, qualitative confirmation and independence. The com pleteness of these logical systems is proven in relation to the standard class of measurable models, which consist of Kripke’s structures in which the accessibility relation is replaced by a probabilistic measure defined over all possible worlds. The second part of the dissertation is about dynamic aspect of confirmation in the sense that we monitor how much the realization of an event affects the realization of another event in the future. Accordingly, in this dissertation we constructed a branchingtime temporal logic with ac tions and probabilistic confirmation operators. The results of the first part were successfully modified to obtain the completeness result of this logic URI: http://hdl.handle.net/123456789/5452 Files in this item: 1
Doktorska_disertacija_sdautovic.pdf ( 1.181Mb ) 
Rašković, Miodrag (Belgrade , 1983)[more][less]
Abstract: The results from this thesis contributed to the development of model theory for probability logic with values in {0,+∞}. The thesis consists of three chapters. The basic notions and theorems from nonstandard analysis and the measure theory are given in Chapter 1. Also, by using the methods of nonstandard analysis, it is proved that if a function f, f:f→R is Lebesque measurable, a function f:R^4→R is continuous and equation f(x+y)=g(f(x),f(y),x,y) holds, then the function f is also continuous. The logics L_ωM, L_ω1M. L_AM and L^5_AM are defined in Chapter 2. The main characteristic of these logics is that their models are σfinite. Some of the axioms of these logics are modifications of known axioms and some of them are new, as the axioms of σfiniteness. The property of completeness, Barwise's completeness and compactness for L_AM are proved. Moreover, the theorem of elementary equivalence, the theorem of Robinson’s coexistence, several theorems of interpolation, upper SkolemLőwenheim theorem and the theorem of normal form are proved. In Chapter 3 of the thesis Loeb measure is founded in the alternative set theory. The theorems which are analogous to some theorems from nonstandard analysis are proved and some limitations of the alternative set theory are presented. Finally, a new proof of the wellknown Lusin's theorem is given. URI: http://hdl.handle.net/123456789/288 Files in this item: 1
phdMRaskovic.pdf ( 3.730Mb ) 
Mršević, Mila (Belgrade)[more][less]

Jovanović, Jelena (Beograd , 2016)[more][less]
Abstract: The subject of this dissertation is a syntactic characterization of congruence ^{ semidistributivity in locally nite varieties by Mal'cev conditions (we consider va rieties of idempotent algebras). We prove that no such characterization is possible by a system of identities including one ternary and any number of binary opera tion symbols. The rst characterization is obtained by a strong Mal'cev condition involving two ternary term symbols: A locally nite variety V satis es congruence meet{semidistributivity if and only if there exist ternary terms p and q (inducing idempotent term operations) such that V satis es p(x; x; y) p(x; y; y) p(x; y; x) q(x; y; x) q(x; x; y) q(y; x; x). This condition is optimal in the sense that the number of terms, their arities and the number of identities are the least possible. The second characterization that we nd uses a single 4ary term symbol and is given by the following strong Mal'cev condition t(y; x; x; x) t(x; y; x; x) t(x; x; y; x) t(x; x; x; y) t(y; y; x; x) t(y; x; y; x) t(x; y; y; x) : The third characterization is given by a complete Mal'cev condition: There exist a binary term t(x; y) and wnuterms !n(x1; : : : ; xn) of variety V such that for all n > 3 the following holds: V j= !n(x; x; : : : ; x; y) t(x; y). URI: http://hdl.handle.net/123456789/4450 Files in this item: 1
disertacijaJelenaJovanovic.pdf ( 1.956Mb ) 
Baković, Vlado (Belgrade , 1976)[more][less]

Mirković, Branislav (Belgrade)[more][less]

Madić, Petar (Belgrade , 1965)[more][less]

Ostrogorski, Tatjana (Belgrade)[more][less]

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 ) 
Stakić, Đorđe (Beograd , 2022)[more][less]
Abstract: Intermodal transport involves traffic with more than one type of trans port. Its presence in practice has become very significant. Bearing in mind that these are mostly long distances, optimization has become important in this area. By default, three standard types of containers of different sizes are used for the transport. In accordance with the given criteria adequate mathematical models have been developed. Based on the model, the exact solver CPLEX was programmed, which succeeds to find the optimal solutions for lesser values of the input parameters. For a number of models, solutions have been implemented in the C programming language. The input data for smaller instances was taken from the practice. To test instances of larger size, the input data is randomly generated from the selected domain. In the first part of this work the main focus is the search for the optimal route in transportation, according to the given criteria, which includes ocean and mainland transport. The problem becomes more complex by increasing the number of shipping companies, the number of side ports, as well as the number of modes of transport on land. In the second part of the paper, additional problems related to the optimization of intermodal transport are considered. More attention is paid to the individual packages by considering the mass and volume of the package, and sub sequently the limits of mass and volume of the containers. One of solved problems is related to the deployment of a large pack in several containers, then the selection of optimal allocation in accordance with the set criteria. The second solved problem is from the aggregate container transport and it is related to the deployment of a large number of packages into containers, taking the constraints of mass and volume into consideration. Here we also seek an optimal allocation in accordance with the set criteria, eg. the total minimum price. The problem thus considered to belong to the heterogeneous and homogeneous vector bin packing. The numerous com puter implementations of exact and approximate methods for the different models are made. Variant methods of Variable Neighborhood Search (VNS) and GRASP (Greedy Randomized Adaptive Search Procedures) have been designed to optimize the aggregate container transport. These approximation methods were compared with each other as well as with solutions obtained by exact solver CPLEX. URI: http://hdl.handle.net/123456789/5377 Files in this item: 1
DjordjeStakicDisertacija.pdf ( 1.629Mb ) 
Zejnullahu, Abdullah (Priština)[more][less]
URI: http://hdl.handle.net/123456789/136 Files in this item: 1
phdAbdullahZejnullahu.pdf ( 1.513Mb ) 
Lazović, Zlatko (Beograd , 2019)[more][less]
Abstract: In the ﬁrst section we present the theory on uniform spaces and measures of noncompactness in metric and uniform spaces. Next, we recall the basic concepts and properties of C∗ and W∗algebras and Hilbert modules over these algebras with some known topologies on Hilbert W∗module. In the second section we construct a local convex topology on the standard Hilbert module l2(A), such that any compact” operator (i.e., any operator in the norm closure of the linear span of the operators of the form maps bounded sets into totally bounded sets. In the biginning A presents unital W∗algebra, leter on A presents unital C∗algebra. The converse is true in the special case where A = B(H) is the full algebra of all bounded linear operators on a Hilbert space H. In the third section we deﬁne a measure of noncompactness λ on the standard Hilbert C∗module l2(A) over a unital C∗algebra, such that λ(E) = 0 if and only if E is Aprecompact (i.e. it is εclose to a ﬁnitely generated projective submodule for any ε > 0) and derive its properties. Further, we consider the known, Kuratowski, Hausdorﬀ and Istratescu measure of noncompactnes on l2(A) regarded as a locally convex space with respect to a suitable topology. We obtain their properties as well as some relationships between them and above introduced measure of noncompactness. In the forth section we generalize the notion of a Fredholm operator to an arbitrary C∗algebra. Namely, we deﬁne ﬁnite type elements in an axiomatic way, and also we deﬁne a Fredholm type element a as such an element of a given C∗algebra for which there are ﬁnite type elements p and q such that (1−q)a(1−p) is invertible. We derive an index theorem for such operators. In subsection Corollaries we show that many wellknown operators are special cases of our theory. Those include: classical Fredholm operators on a Hilbert space, Fredholm operators in the sense of Breuer, Atiyah and Singer on a properly inﬁnite von Neumann algebra, and Fredholm operators on Hilbert C∗modules over a unital C∗algebra in the sense of Mishchenko and Fomenko. URI: http://hdl.handle.net/123456789/4819 Files in this item: 1
dr_Zlatko_Lazovic.pdf ( 2.019Mb ) 
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]