Auflistung Doctoral Dissertations nach Titel
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Ašić, Miroslav (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/349 Dateien zu dieser Ressource: 1
phdMiroslavAsic.pdf ( 4.813Mb ) -
Milovanović, Zorica (Beograd , 2015)[more][less]
Zusammenfassung: U primenama, naro cito u in zenjerstvu, cesto se sre cu kompozitne ili slojevite strukture, pri cemu se osobine pojedinih slojeva mogu zna cajno razlikovati od osobina okolnog materijala. Slojevi mogu imati strukturnu, termi cku, elektromagnetsku ili opti cku ulogu itd. Matemati ckim modelovanjem prenosa energije i mase u oblastima sa slojevima dobijaju se tzv. transmisioni problemi. Na samom po cetku, u disertaciji se razmatra transmisioni spektralni problem u oblasti koja se sastoji od dva disjunktna intervala. Na svakom intervalu zadat je problem sopstvenih vrednosti, dok se interakcija izmed u njihovih re senja opisuje nelokalnim uslovima saglasnosti. Dokazana je egzistencija prebrojivog niza generalisanih re senja, pri cemu ured eni parovi sopstvenih funkcija pripadaju odgovaraju cim prostorima Soboljeva. Opisana je struktura spektra i asimptotsko pona sanje sopstvenih vrednosti. Konstruisana je diferencijska shema za njihovo re savanje. Pored transmisionog spektralnog problema, u disertaciji se razmatraju klase nestandardnih elipti ckih i paraboli ckih transmisionih problema u disjunktnim oblastima. Kao modelni primer uzeta je oblast koja se sastoji iz dva nesusedna pravougaonika. U svakoj podoblasti zadat je grani cni problem elipti ckog tipa, odnosno po cetnograni cni problem paraboli ckog tipa. Interakcija izmed u re senja opisuje se pomo cu nelokalnih uslova saglasnosti na granicama posmatranih podoblasti. Razmotreno je vi se primera zi ckih i in zenjerskih zadataka koji se svode na transmisione probleme sli cnog tipa. Za modelne probleme dokazana je egzistencija i jedinstvenost re senja u odgovaraju cim prostorima Soboljeva. Takod e su konstruisane diferencijske sheme za njihovo re URI: http://hdl.handle.net/123456789/3999 Dateien zu dieser Ressource: 1
phdZoricaMilovanovic.pdf ( 8.476Mb ) -
Isaković-Ilić, Mirjana (Belgrade)[more][less]
Zusammenfassung: In this thesis cut elimination and decidability for several propositional substructural logics are studied. The thesis consists of nine chapters. Chapters 2-6 make the first part of the thesis. In that part sequent systems for substrictural logics are formulated. In Chapters 3 and 4 for each of these systems an algebraic structure is given and completeness and consistency are proved. In Chapters 5 and 6 cut elimination and decidability for these systems are studied. It is well known that sequent system of classical Lambek logic, the system SL is decidable and that cut is not an admissible rule in CL. Another sequent system for classical Lambek logic, the system CL* is formulated, and the elimination of cut in CL* is proved. The system CL* does not posses the subformula property, so decidability for classical Lambek logic is not the direct consequence of the cut-elimination procedure in CL*. However, on the basis of the cut elimination procedure in CL*, a procedure for deciding of whether a sequent is provable in CL* or not is given (i. e., a new (pure syntactic) proof of decidability for classical Lambek logic is given). The same result is shown for classical Lambek logic with weakening. In the second part of the thesis (chapters 7-9), by using that proof, an algorithm (based on the tableau method) is formulated for deciding whether or not a formula is the theorem in any of considered substructural logics. URI: http://hdl.handle.net/123456789/201 Dateien zu dieser Ressource: 1
phdMirjanaIsakovicIlic.pdf ( 1.047Mb ) -
Mosurović, Milenko (Belgrade)[more][less]
Zusammenfassung: The results of this thesis are connected with papers of Wolter and Zakharyashchev in which various expressive and decidable description logics with epistemic, temporal, and dynamic operators are constructed, but the complexity of the satisfaction problem in these logics has remained unclear. The thesis consists of seven chapters. Chapter 1 and 5 contain the notions and properties which are used in other chapters. In Chapter 2 a fragment of the logic DIF, which is called D_1IF , is considered and new constructions and proofs for that logic are given. In Chapter 3 a fragment of the logic DIO, which is called D_1IO, is studied. In Chapter 4 by using the results from Chapter 2 and Chapter 3 NEXPTIME algorithm, which tests whether a structure simple quasi-world or not, is constructed and it is used in Chapter 7. In Chapters 6 and 7 it is shown that the modal description logics of Wolter and Zakharyashchev based on arbitrary frames are NEXPTIME-complete, no matter whether the underlying description logic is ALC, CI or C_1IQ. Moreover, it is shown that these logics based on S5-frames (for knowledge), and KD45-frames (for beliefs) are also NEXPTIME-complete. Finally, the following property is shown: the description logics of Wolter and Zakharyashchev based on N-frames (for time) are EXPSPACE-complete, no matter whether the underlying description logic is ALC_U, CI_U or C_1IQ_U. URI: http://hdl.handle.net/123456789/192 Dateien zu dieser Ressource: 1
phdMilenkoMosurovic.pdf ( 3.024Mb ) -
Kanan, Asmaa (Beograd , 2013)[more][less]
Zusammenfassung: Semiring with zero and identity is an algebraic structure which generalizes a ring. Namely, while a ring under addition is a group, a semiring is only a monoid. The lack of substraction makes this structure far more difficult for investigation than a ring. The subject of investigation in this thesis are matrices over commutative semirings (wiht zero and identity). Motivation for this study is contained in an attempt to determine which properties for matrices over commutative rings may be extended to matrices over commutative semirings, and, also, which is closely connected to this question, how can the properties of modules over rings be extended to semimodules over semirings. One may distinguish three types of the obtained results. First, the known results concerning dimension of spaces of n-tuples of elements from a semiring are extended to a new class of semirings from the known ones until now, and some errors from a paper by other authors are corrected. This question is closely related to the question of invertibility of matrices over semirings. Second type of results concerns investigation of zero divisors in a semiring of all matrices over commutative semirings, in particular for a class of inverse semirings (which are those semirings for which there exists some sort of a generalized inverse with respect to addition). Because of the lack of substraction, one cannot use the determinant, as in the case of matrices over commutative semirings, but, because of the fact that the semirings in question are inverse semirings, it is possible to define some sort of determinant in this case, which allows the formulation of corresponding results in this case. It is interesting that for a class of matrices for which the results are obtained, left and right zero divisors may differ, which is not the case for commutative rings. The third type of results is about the question of introducing a new rank for matrices over commutative semirings. For such matrices, there already exists a number of rank functions, generalizing the rank function for matrices over fields. In this thesis, a new rank function is proposed, which is based on the permanent, which is possible to define for semirings, unlike the determinant, and which has good enough properties to allow a definition of rank in such a way. URI: http://hdl.handle.net/123456789/4274 Dateien zu dieser Ressource: 1
phdKanan_Asmaa.pdf ( 1.221Mb ) -
Dedagić, Fehim (Priština)[more][less]
URI: http://hdl.handle.net/123456789/43 Dateien zu dieser Ressource: 1
phdFehimDedagic.pdf ( 2.250Mb ) -
Karapetrović, Boban (Beograd , 2017)[more][less]
Zusammenfassung: In this thesis, we study the in nite Hilbert matrix viewed as an operator, called the Hilbert matrix operator and denoted by H and Libera operator, denoted by L, on the classical spaces of holomorphic functions on the unit disk in the complex plane. It is well known that the Hilbert matrix operator H is a bounded operator from the Bergman space Ap into Ap if and only if 2 < p < 1. Also, it is known that the norm of the Hilbert matrix operator H on the Bergman space Ap is equal sin 2 p , when 4 p < 1, and it was conjectured that kHkAp!Ap = sin 2 p ; when 2 < p < 4. In this thesis we prove this conjecture. We nd the lower bound for the norm of the Hilbert matrix operator H on the weighted Bergman space Ap; , kHkAp; !Ap; sin ( +2) p ; for 1 < + 2 < p: We show that if 4 2( + 2) p, then kHkAp; !Ap; = sin ( +2) p ; while in the case 2 +2 < p < 2( +2), upper bound for the norm kHkAp; !Ap; , better then known, is obtained. We prove that the Hilbert matrix operator H is bounded on the Besov spaces Hp;q; if and only if 0 < p; ; = 1 p + 1 < 1. In particular, operator H is bounded on the Bergman space Ap; if and only if 1 < + 2 < p and it is bounded on the Dirichlet space Dp = Ap; 1 if and only if maxf1; p 2g < < 2p 2. We also show that if > 2 and 0 < " 2, then the logarithmically weighted Bergman space A2 log is mapped by the Hilbert matrix operator H into the space A2 log 2" . If 2 R, then the Hilbert matrix operator H maps logarithmically weighted Bloch space Blog into Blog +1. We also prove that operator H maps logarithmically weighted Hardy-Bloch space B1 log , when 0, into B1 log 1 and that this result is sharp. Also, we have that the space VMOA is not mapped by the Hilbert matrix operator H into the Bloch space B. On the other hand, we nd that the Libera operator L is bounded on the Besov space Hp;q; if and only if 0 < p; ; = 1 p + 1. Then, we prove that if > 1, then the logarithmically weighted Bergman space A2 log is mapped by the Libera operator L into the space A2 log 1 , while if 2 R, then the Libera operator L maps logarithmically weighted Bloch space Blog into itself. If > 0, we have that operator L maps logarithmically weighted Hardy-Bloch space B1 log into B1 log 1 and we show that this result is sharp. The well known conjecture due to Korenblum about maximum principle in Bergman space Ap states: Let 0 < p < 1. Then there exists a constant 0 < c < 1 with the following property. If f and g are holomorphic functions in the unit disk D, such that jf(z)j jg(z)j for all c < jzj < 1, then kfkAp kgkAp . Hayman proved Korenblum's conjecture for p = 2 and Hinkkanen generalized this result, by proving conjecture for all 1 p < 1. The case 0 < p < 1 of conjecture still remains open. In this thesis we resolve this case of the Korenblum's conjecture, by proving that Korenblum's maximum principle in Bergman space Ap does not hold when 0 < p < 1. URI: http://hdl.handle.net/123456789/4497 Dateien zu dieser Ressource: 1
Boban_Karapetrovic_doktorska_disertacija.pdf ( 1.392Mb ) -
Filipović, Vladimir (Beograd , 2006)[more][less]
URI: http://hdl.handle.net/123456789/2478 Dateien zu dieser Ressource: 1
phdFilipovicVladimir.pdf ( 2.145Mb ) -
Ivković, Zoran (Belgrade , 1964)[more][less]
URI: http://hdl.handle.net/123456789/216 Dateien zu dieser Ressource: 1
phdZoranIvkovic.pdf ( 1.731Mb ) -
Kalajdžić, Gojko (Belgrade , 1982)[more][less]
URI: http://hdl.handle.net/123456789/328 Dateien zu dieser Ressource: 1
phdGojkoKalajdzic.pdf ( 5.755Mb ) -
Makragić, Milica (Beograd , 2018)[more][less]
Zusammenfassung: This doctoral dissertation comprises two parts. Trigonometric polynomial rings are the central topic of the first part of the dissertation. It is presented that the ring of complex trigonometric polynomials, C [cos x, sin x ], is a unique factorization domain, and that the ring of real trigonometric polynomials, R [cos x, sin x ], is not a unique factorization domain. Necessary and sufficient conditions for the case when in the ring C [cos x, sin x ], unlike the ring R [cos x, sin x ], the degree of the product of two trigonometric polynomials is not equal to the sum of degrees of its factors, are given. The theory of trigonometric polynomials is extended to hyperbolic-trigonometric polynomials, or HT-polynomials for short, which are defined similarly to trigonome- tric polynomials. Real or complex HT-polynomials form a ring and even an integral domain R [cosh x, sinh x ], or C [cosh x, sinh x ]. Factorization in these domains is con- sidered, and it is shown that these are unique factorization domains. The irreducible elements, as well as the form of the maximal ideals of both these domains are deter- mined. The algorithms for dividing, factoring, computing greatest common divisors, as well as the algorithms for simplifying ratios of two HT-polynomials are considered over the field of rational numbers. In the second part of the dissertation, related to applications, two methods of proving inequalities of the form f ( x ) > 0 are described over the given finite in- terval ( a,b ) ⊂ R , a ≤ 0 ≤ b , which by using the finite Maclaurin series expan- sion generate polynomial approximations, when the function f ( x ) is element of the ring extension of R [cos x, sin x ], or R [cosh x, sinh x ], denoted by R [ x, cos x, sin x ], or R [ x, cosh x, sinh x ]. The completeness of the presented methods is proved and the concrete results of these methods are illustrated through examples of proving actual inequalities. URI: http://hdl.handle.net/123456789/4745 Dateien zu dieser Ressource: 1
Disertacija_Milica_Makragic.pdf ( 2.169Mb ) -
Bajšanski, Bogdan (Novi Sad)[more][less]
URI: http://hdl.handle.net/123456789/137 Dateien zu dieser Ressource: 1
phdBogdanMBajsanski.pdf ( 1.575Mb ) -
Marković, Sima (Belgrade , 1912)[more][less]
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Ajajbegović, Jusuf (Sarajevo)[more][less]
URI: http://hdl.handle.net/123456789/156 Dateien zu dieser Ressource: 1
phdJusufAlajbegovicpdf.pdf ( 3.012Mb ) -
Erić, Lj. Aleksandra (Belgrade , 2012)[more][less]
Zusammenfassung: This thesis concerns P-vertices and P-set of non-singular acyclic matrices A and also singular acyclic matrices. It was shown that each singular matrix of order n has at most n ¡ 2 P-vertices. Also, it is shown that this does not hold for non-singular acyclic matrices by constructing non-singular acyclic matrices whose graphs are T having n¡1 ( or n) P-vertices. These matrices also achieve maximum size of P-set over non-singular acyclic matrices whose graphs are T. In this thesis, there is classi¯cation of the trees for which there is non- singular matrix where each vertex is P-vertex. In particular, it is shown that such trees have an even number of vertices. Both results provide answer to questions proposed by I.-J. Kim and B. L. Shader. In the end, related classi¯cations on non-singular trees with the size of a P-set bounded are addressed. Also, it is shown that double star DSn with n vertices, is an example of a tree such that, for each non-singular matrix A whose graph is DSn the number of P-vertices of A is less than n¡2. This example provides a positive answer to a question proposed recently by Kim and Shader. A recent classi¯cation of those trees for which each of associated acyclic matrices has distinct eigenvalues whenever the diagonal entries are distinct was established. Here is analyze of maximum number of distinct diagonal entries, and corresponding location, in order to preserve that multiplicity characterization. Recently, the multiplicities of eigenvalues of ©-binary tree was analyzed. This paper carry this discussion forward extending their results to larger family of trees, namely, the wide double path, a tree consisting of two paths that are joined by another path. Some introductory considerations for dumbbell graphs are mentioned re- garding the maximum multiplicity of the eigenvalues. URI: http://hdl.handle.net/123456789/2488 Dateien zu dieser Ressource: 1
Eric_Aleksandra.pdf ( 2.125Mb ) -
Vučetić, Milica (Beograd , 2017)[more][less]
Zusammenfassung: In this dissertation we discuss in uence of H emission from supernova remnants (SNRs) on H derived star formation rates (SFRs). We present the detection of 16 optical SNR candidates in a part of nearby spiral galaxy IC342, and two more poten- tial SNRs in NGC 185 galaxy. The candidates were detected by applying [S ii]/H ratio criterion on observations made with the 2 m telescope at Rozhen National Astronomical Observatory in Bulgaria. Also, in this dissertation we present the most up-to-date list of nearby galaxies with optically detected SNRs. When deri- ving H star formation rates, assumption is that the radiation is coming from the ionized gas surrounding hot and young stars { Hii regions. In this case, emission from SNRs contaminates H ux used to derive SFR. We found that the contribu- tion of SNRs' ux to the total H ux, for 18 galaxies in our sample of galaxies with optical SNRs, is 5 5%. Due to the observational selection effects, the SNR contamination of SFRs derived herein represents only a lower limit. M83 is the galaxy with the most detected optical SNRs and in this galaxy SNRs account for 9 per cent of the total H emission. We expect that fraction similar to this would be close to the real contribution of SNR emission to the total H emission in spiral galaxies. Using two dwarf galaxies as an example, Holmberg IX and NGC 185, we show that the contamination of H ux by SNRs, or other sources, can be much larger, up to ten times higher than total H ux coming from Hii regions of the observed galaxy. URI: http://hdl.handle.net/123456789/4501 Dateien zu dieser Ressource: 1
Milica_disertacija_21.03.2017.pdf ( 26.28Mb ) -
Vučetić, Milica (Beograd , 2017)[more][less]
Zusammenfassung: In this dissertation we discuss in uence of H emission from supernova remnants (SNRs) on H derived star formation rates (SFRs). We present the detection of 16 optical SNR candidates in a part of nearby spiral galaxy IC342, and two more poten- tial SNRs in NGC 185 galaxy. The candidates were detected by applying [S ii]/H ratio criterion on observations made with the 2 m telescope at Rozhen National Astronomical Observatory in Bulgaria. Also, in this dissertation we present the most up-to-date list of nearby galaxies with optically detected SNRs. When deri- ving H star formation rates, assumption is that the radiation is coming from the ionized gas surrounding hot and young stars { Hii regions. In this case, emission from SNRs contaminates H ux used to derive SFR. We found that the contribu- tion of SNRs' ux to the total H ux, for 18 galaxies in our sample of galaxies with optical SNRs, is 5 5%. Due to the observational selection effects, the SNR contamination of SFRs derived herein represents only a lower limit. M83 is the galaxy with the most detected optical SNRs and in this galaxy SNRs account for 9 per cent of the total H emission. We expect that fraction similar to this would be close to the real contribution of SNR emission to the total H emission in spiral galaxies. Using two dwarf galaxies as an example, Holmberg IX and NGC 185, we show that the contamination of H ux by SNRs, or other sources, can be much larger, up to ten times higher than total H ux coming from Hii regions of the observed galaxy. URI: http://hdl.handle.net/123456789/4507 Dateien zu dieser Ressource: 1
Milica_disertacija_21.03.2017.pdf ( 26.28Mb ) -
Vučković, Vesna (Univerzitet u Beogradu – Matematički fakultet , 2010)[more][less]
Zusammenfassung: This dissertation deals with digital watermark for grayscale images. Digital watermark in copyright protection needs to satisfy detectability and fidelity conditions. If watermark is embedded stronger, it will be likely detectable, but it will be noticeable too, and it will jeopardize host image quality. Here, for a well known, AWGN watermark, optimal embedding strength (minimal which guaranties watermark detectability) is determined. Optimal strength is analyzed - for effective embedding (watermark needs to be detectable immediately after embedding) - for watermark to be robust against expected modification (it needs to be detectable in image which will be after embedding subjected to this modification) For effective AWGN watermark embedding, mathematical formula for optimal strength calculating is derived. For watermark robust against expected modification, one algorithm for optimal strength is given. Among all image modifications (valumetric and geometric), lossy compression surely has an important place. Images which nowadays we can find on Net are mostly in some lossy compressed form. In such circumstances, embedded watermark will also surely be exposed to lossy compression. This is why in this dissertation particular attention is devoted to lossy compression. Thus, its considerable part deals with AWGN watermark optimal strength, in spatial and in transform domains. Specially, here is analyzed embedding in some image subchannels in the block DCT domain, and quantization noise impact on the embedded watermark message. URI: http://hdl.handle.net/123456789/1073 Dateien zu dieser Ressource: 1
PhDVVuckovic.pdf ( 4.249Mb ) -
Banjević, Dragan (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/287 Dateien zu dieser Ressource: 1
phdDraganBanjevic.pdf ( 3.032Mb ) -
Šestak, Ivan (Belgrade , 1987)[more][less]
URI: http://hdl.handle.net/123456789/240 Dateien zu dieser Ressource: 1
phdIvanSestak.PDF ( 2.046Mb )