Browsing Doctoral Dissertations by Title

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 ) 
Dražić, Zorica (Beograd , 2014)[more][less]
Abstract: The Variable neighborhood search method proved to be very successful for solving discrete and continuous optimization problems. The basic idea is a systematic change of neighborhood structures in search for the better solution. For optimiza tion of multiple variable functions, methods for obtaining the local minimum starting from certain initial point are used. In case when the continuous function has many local minima, nding the global minimum is usually not an easy task since the obta ined local minima in most cases are not optimal. In typical implementations with bounded neighborhoods of various diameters it is not possible, from arbitrary point, to reach all points in solution space. Consequently, the strategy of using the nite number of neighborhoods is suitable for problems with solutions belonging to some known bounded subset of IRn. In order to overcome the previously mentioned limitation the new variant of the method is proposed, Gaussian Variable neighborhood search method. Instead of de ning the sequence of di erent neighborhoods from which the random point will be chosen, all neighborhoods coincide with the whole solution space, but with di e rent probability distributions of Gaussian type. With this approach, from arbitrary point another more distant point is theoretically reachable, although with smaller probability. In basic version of Variable neighborhood search method one must de ne in advance the neighborhood structure system, their number and size, as well as the type of random distribution to be used for obtaining the random point from it. Gaussian Variable neighborhood search method has less parameters since all the neighborhoods are theoretically the same (equal to the solution space), and uses only one distribution family  Gaussian multivariate distribution with variable dispersion. File transfer scheduling problem (FTSP) is an optimization problem widely appli cable to many areas such as Wide Area computer Networks (WAN), Local Area Ne v tworks (LAN), telecommunications, multiprocessor scheduling in a MIMD machines, task assignments in companies, etc. As it belongs to the NPhard class of problems, heuristic methods are usually used for solving this kind of problems. The problem is to minimize the overall time needed to transfer all les to their destinations for a given collection of various sized les in a computer network, i.e. to nd the le transfer schedule with minimal length. In order to obtain the exact solution of the FTS problem, integer linear pro gramming formulations are proposed and their correctness is proved. In this way optimal solutions can be found for small and medium size test instances. For large test instances, the Variable neighborhood search method is proposed using the "permutation" representation and typical neighborhood structures. More over, the same method is used for obtaining the upper bounds of the solutions which are used in proposed integer linear programming formulations. For obtaining be tter solutions in the small neighborhood of the current solution, three di erent local search procedures are implemented: 2swap, 2swap adjacent and variable neighbo rhood descent. In order to apply the continuous optimization methods for solving FTSP, the weighted solution representation is developed. Such representation enables the co ntinuous optimization methods to be used, which do not require the di erentiability of objective function. Since Gauss Variable neighborhood search method proved to be successful in continuous optimization problems, it was applied to FTSP. Pre viously described local search procedures can also be used with weighted solution representation. Using the proposed methods optimal solutions for all small and medium size test instances are found. For large size instances, which are beyond the reach of exact methods, metaheuristic methods obtained good solutions in reasonable time. URI: http://hdl.handle.net/123456789/4246 Files in this item: 1
phdDrazic_Zorica.pdf ( 4.739Mb ) 
Mihajlović, Borivoje (Belgrade , 1964)[more][less]
URI: http://hdl.handle.net/123456789/227 Files in this item: 1
phdBorivojeMihajlovic.pdf ( 2.509Mb ) 
Manojlović, Vesna (Beograd , 2008)[more][less]

Nikolić, Silvana (Belgrade)[more][less]

Marjanović, Miroslav (Belgrade)[more][less]

Kamberi, Qerim (Priština)[more][less]

Janković, Slobodan (Beograd , 1979)[more][less]

Marković, Marijan (Belgrade , 2013)[more][less]
Abstract: This work consists of three chapters. The first one contains some well known facts about Hardy classes of harmonic, analytic, and logarithmically subharmonic functions in the unit disk, as well as their applications. Then we briefly talk about the harmonic and minimal surfaces, the classical isoperimetric inequality, and the more recent results related to this inequality. One of the most elegant way to establish the isoperimetric inequality is via Carleman’s inequality for analytic functions in disks. In the second chapter we present the results from our recent work [29] for harmonic mappings of a disc onto a Jordan surface. In this chapter we establish the versions of classical theorems of Carath´eodory and Smirnov for mappings of the previous type. At the end of the head we apply these results to prove the isoperimetric inequality for Jordan harmonic surfaces bounded by rectifiable curves. In the third chapter, according to the author paper [35], we prove an inequality of the isoperimetric type, similar to Carleman’s, for functions of several variables. The first version of this inequality is for analytic functions in a Reinhardt domain. The second one concerns the functions that belong to Hardy spaces in polydiscs. URI: http://hdl.handle.net/123456789/2586 Files in this item: 1
Markovic_Marijan.pdf ( 709.3Kb ) 
Kovačević, Ilija (Belgrade)[more][less]

Gilezan, Koriolan (Belgrade)[more][less]

Jovanović, Boško (Belgrade)[more][less]

Hoxha, Isak (Priština)[more][less]

Mihajlović, Bojana (Beograd , 2016)[more][less]
Abstract: The subject of this dissertation belongs to scientific field of spectral graph theory, a young branch of mathematical combinatorics, i.e. graph theory, which finds important applications in many areas, such as chemistry, physics, computer science, telecommunications, sociology, etc., and various fields of mathematics. Spectral graph theory connects basic properties and the structure of a graph with characteristics of the spectra of its matrices (adjacency matrix, Laplacian matrix, etc.). In this dissertation we only work with the adjacency matrix. The second largest eigenvalue of the adjacency matrix of a graph (or, simply, second largest eigenvalue of a graph), as well as its distance from the largest eigenvalue, are very important especially in applications of spectral graph theory in computer science. The property of a graph that one of its eigenvalues does not exceed some given value is a hereditary one; therefore, many of the investigations of this kind have been directed at finding the maximal allowed graphs, or minimal forbidden graphs for that property. In this dissertation we determine some classes of graphs whose second largest eigenvalue does not exceed some given value, and, for that purpose, we develop some very useful tools. In methodological sense, investigations in this dissertation represent a combined approach consisting of application of the algebraic apparatus and methods of spectral graph theory and combinatorial reasoning, whilst at some stages the expert system newGRAPH has been used. The dissertation consists of eight chapters, each of which is divided into subchapters. In the beginning, some important previous work is shown, and afterwards we present some original elements of the algebraic and combinatorial apparatus that speed up and simplify the further work. We define some mappings between certain families of graphs, some of which preserve the sign of the expression 2 2 , and, using them, we describe and systematize some (already known) results in a new way. Further on we completely determine all maximal reflexive tricyclic cacti which are not RSdecidable and whose cycles do not form a bundle, from the classes 1 R and 3 R , and we give some partial results about the class 2 R , using previously induced mappings (until now only the graphs from the remaining class 4 R have been completely determined [40], [46]). Next, we completely describe all minimal forbidden graphs in the class of bicyclic graphs with a bridge, and all minimal forbidden graphs in the class 3 R  the approach that so far has never been used with reflexive graphs. Then we determine the maximal number of the cycles for RSundecidable reflexive cacti whose cycles do form a bundle, and, therefore, generally for RSundecidable reflexive cacti and we describe three classes of maximal reflexive RSundecidable reflexive cacti that contain a bundle. Further on, some of the previous results are generalized: the generalized RStheorem is stated and proved (socalled GRStheorem) for any r , r 0 ; previously induced mappings are generalized, their properties are proved and various examples of classes of graphs with the property 2 r (for r 0 ) are given. Based on this, we describe all GRSundecidable maximal graphs for the property 2 2 in the class of unicyclic and multicyclic graphs, and also all RSundecidable maximal θgraphs for this property as well as all GRSundecidable maximal trees with the property 2 5 1 2 . Furthermore, we investigate the limit 3 (as in [28]) and we describe all trees with the diameter 3 and the diameter larger than 8, with the property 2 3 , as well as all GRSundecidable multicyclic cacti with the same property. Finally, we introduce and apply socalled σmodifications of Smith trees. We describe seven σmodifications and corresponding extensions, and we notice the appearance in (already known) results in the class of multicyclic reflexive cacti with 4 cycles. Applying some extensions to certain families of tricyclic cacti, we obtained the results in the class of multicyclic reflexive cacti with 4 cycles, using a different approach [48]. Finally, in the conclusion, we suggest some possible directions of further investigations. URI: http://hdl.handle.net/123456789/4445 Files in this item: 1
Mihailovic_Bojana.pdf ( 6.960Mb ) 
Acketa, Dragan (Novi Sad , 1984)[more][less]

Vučemilović, Ante (Belgrade)[more][less]

Cerović, Blagoje (Novi Sad , 1982)[more][less]

Crvenković, Siniša (Novi Sad , 1981)[more][less]
Abstract: Teorija semigrupa razvija se kao samostalna °blast savremene algebre, Predmet izu6avanja teorije semigrupa su razne kiase semigrupa tj. semigrupe koje zadovoljavaju dati uslov. U ovom radu razmatramo semigrupe iz nekih podklasa kiase regularnih semigrupa. Pojam regularnosti, koji je uveo J. von Neumann [31] za prstene, su Thierrin i BarHep preneli u teoriju semigrupa 6to se pokazalo zna6ajnim za razvoj teorije semigrupa umAte. Ovde se posebno ispituje jedna podklasa kiase kompletno regularnih semigrupa tzv. klasa (m,n)*antiinverznih semigrupa. Ova klasa obuhvata klasu antiinverznih semigrupa ill Pojam bazisne kiase, neke klase semigrupa, uveo je E.C. JThnHH [25]. U radu odredjujemo bazisne kiase za razne kiase semigrupa. Zna6ajnu klasu semigrupa 6ine polumr0e. P.M. Cohn [9] i C. Pe6aHe su 1965. godine pokazali da je svaka algebra podalgebra neke semigrupe. U Glavi IV opisujemo klasu algebri koje su podalgebre polumrea. U Glavi I su navedeni elementarni pojmovi o semigrupama, grupama, algebrama, idealima, kongruencijama, itd. Dati Virtual Library of Faculty of Mathematics  University of Belgrade elibrary.matf.bg.ac.rs ii su dokazi nekih teorema koje se koriste u radu. Ovaj materijal uzet je iz [7] i [22]. Takodje, dat je dokaz G. upone za teoremu CohnPe6aHe. U Glavi II ispituju se (m,n)*antiinverzne semigrupe. Materijal ove glave preuzet je iz [ 61, [11] i [12]. U ta6ki 2. date su neke dekompozicije (m,n)*antiinverznih semigrupa. Teorema 2.3. glavni je rezultat ove glave. Greenove relacije razmatraju se u ta6ki 3. Dobija se niz karakterizaci  ja semigrupa iz klase m,n . Na kraju Glave II navedena su tvrdjenja Eiji dokazi su izostavljeni jer su sli6ni dokazima teorema u [ 21. U Glavi III ispituju se bazisne klase raznih klasa semigrupa. Dat je algoritam kojim odredjujemo bazisnu klasu bilo koje klase (m,n)*antiinverznih semigrupa. Primeri bazisnih klasa za razne semigrupe dati su u ta6ki 2. Materim, n jal za take 1. i 2. uzet je iz [121. U ta6ki 3. razmatraju se QS* (OS ) semigrupe tj. semigrupe nje sve prave podsemi  m,n m,n grupe pripadaju klasi m,n (Sm,n ). Teoremom 3.1. data je karakterizacija semigrupa klase QS*m,n (QS m,n ). Problem egzistencije bazisne klase semigrupa ije sve prave podsemigrupe zadovoljavaju uslov oblika (Vx)(By)4)(x,y) re§en je u ta6ki 4. Na kraju 4. data je nekoliko primera. Materijal iz ta6aka 3. i 4. ovde je prvi put izloen. U Glavi IV opisane su podalgebre polumr0a. Potreban i dovoljan uslov da neka algebra bude podalgebra polumree dat je u taCki 1. Lema 1.3. je kljufta lema u dokazu teoreme 1.1. Virtual Library of Faculty of Mathematics  University of Belgrade elibrary.matf.bg.ac.rs iii Dokaz ove leme izvodi se koristedi pojam transformacije U tadki 2. navedeni su neki specijalni sludajevi koji su neposredna posledica teoreme 1.1. Materijal za ovu glavu uzet je iz [18]. Literatura koja je korigdena u ovom radu navedena je na kraju i 6ine je 44 bibliografske jedinice. Dr Stojan Bogdanovid svojim idejama i savetima pornogao mi je pri izradi ovog rada zbog 6eqa mu dugujem trajnu zahvalnost. Akademik profesor (op( 11 HynoHa velikodugno je pristao na saradnju sa autorom ovog rada. Zahvaljujem se profesoru 6to je prihvatio moju saradnju i omogudio mi da rezultato zajedni6kocr rada izlo2im u Glavi IV. Profesor Svetozar Milid prihvatio se da bude mentor pri izradi ove disertacije. Imam prijatnu du2nost da se zahvalim profesoru Milidu za nesebi6nu pa2nju koju posvedije mom radu. URI: http://hdl.handle.net/123456789/4094 Files in this item: 1
Neke_klase_semigrupa.PDF ( 10.42Mb ) 
Crvenković, Siniša (Novi Sad , 1981)[more][less]