Browsing Doctoral Dissertations by Title
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Dmitrović, Dušica (Beograd , 2026)[more][less]
Abstract: The study of integral means of the composition of functions defined on the unit disk D in the complex plane dates back to the 1920s, with one of the earliest results in this area being Littlewood’s subordination principle. When investigating the norm of composition operators on certain spaces of holomorphic functions, a natural need arises to study the relationship between the integral means of the composition f ◦ φ and those of the function f itself. Littlewood’s principle is one of the main tools used to establish this connection. However, it is not the only one. In this dissertation, additional methods for studying the relationship between these integral means are presented. By applying these methods, two-sided estimates for the norm of the composition operator Cφ on spaces of mixed norm Hp,q,α are obtained in the form K1 ≤ ∥ Cφ ∥Hp,q,α→Hp,q,α ≤ K2, where the constants K1 and K2 depend on the parameters p, q, α and |φ(0)|. Furthermore, the monotonicity of the integral mean of a holomorphic function f on the unit disk D, denoted by Mp,q,α[f ](ρ, R, s) , is investigated, where 0 < p, q, α < ∞, 0 ≤ ρ < R ≤ 1 and 0 ≤ s ≤ 1. One consequence of this result is the monotonicity of the norm ∥f ∥p,q,α in mixed norm spaces with respect to the parameters p, q, α. One of the operators that can be represented as an integral of weighted composition operators Tt is the Hilbert matrix operator H acting on the weighted Bergman spaces Ap γ . Moreover, it is known that the operator H is bounded if and only if 1 < γ + 2 < p, and in this case, the following lower bound for the norm of the operator holds: ∥H∥Ap γ →Ap γ ≥ π/ sin (γ+2)π p . When γ > 0 and p ≥ 2(γ + 2), it is known that the norm is equal to this constant. In studying the norm of the operator H, after applying Minkowski’s theorem, the application of Minkowski’s inequality reduces the problem to estimating the norm of the operator Tt. As a result of this analysis, in the case where γ < 0 a new upper bound for the norm of the operator H is obtained, while in the case where γ > 0, the interval on which the norm equals the constant π/ sin (γ+2)π p is extended. Finally, the dissertation presents a refinement of Littlewood’s subordination principle under an additional injectivity assumption, together with applications of the new inequality to the Rogosinski theorem and to norm estimates for compositions of functions on weighted Bergman spaces. URI: http://hdl.handle.net/123456789/5783 Files in this item: 1
Dusica_Dmitrovic_doktorska_disertacija.pdf ( 1.895Mb ) -
Shafah, Osama (Belgrade , 2013)[more][less]
Abstract: In this thesis we will give an interesting relation between finite rings and their graphs, such relations are obtained in following way. Consider a directed graph on a finite ring , where are sets of vertices and edges respectively, and defined by . Since is finite, it has an integer characteristic . If is not a prime, then has zero divisors and is not a unique factorization ring, but if it is prime, then nevertheless could have zero-divisors (e.g., ). Let and be relatively prime numbers, such that , ! and define two maps " #, $ by " %& and %& respectively, so " and are homomorphism maps, suppose that '() *+,-. / + is a directed cycle of length . in a directed graph , then many interesting algebraic relations will exist between longest cycles in , # and $, which will be shown up in the chapter III. URI: http://hdl.handle.net/123456789/3052 Files in this item: 1
Doctroral_theiss_Osama_Shafah.pdf ( 332.8Kb ) -
Turku, Haljilj (Pristina , 1978)[more][less]
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Pažanin, Ratomir (Belgrade , 1980)[more][less]
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Stojanović, Milan (Beograd , 2017)[more][less]
Abstract: The goal of this dissertation is to determine values of local dynamical constants. This goal is achieved through examination of multiple samples of selected stars near the Sun. The selection is done by using planar and vertical eccentricities as sampling criteria. The solution for calculating eccentricities is given. In the next step a large sample of stars is selected by defining upper limits for eccentricities and vertical amplitude. Then nested subsamples are formed in two ways: in the first one upper eccentricity limit is subjected to decreasing, in the other one this is the case with upper amplitude of oscillations perpendicular to the plane. The values of the local dynamical constants are deduced by analysing this material. URI: http://hdl.handle.net/123456789/4498 Files in this item: 1
Stojanovic_Milan_teza.pdf ( 8.577Mb ) -
Sadžakov, Sofija (Belgrade)[more][less]
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Lelas, Nikola (Beograd , 2022)[more][less]
Abstract: The subject of the dissertation is the problem of simultaneous nonvanishing of quadratic twists of elliptic curve 𝐿-functions and quadratic Dirichlet 𝐿-functions (and their derivatives) at the centar point 𝑠 = 1 2 , in the situation when these objects are defined over the rational function field over finite field F𝑞. For each monic polynomial 𝐷 ∈ F𝑞 [𝑡], there is a corresponding quadratic Dirichlet character 𝜒𝐷. Associated to such character, there is the corresponding Dirichlet 𝐿- function 𝐿(𝑠, 𝜒𝐷), as well as the quadratic twist 𝐸 ⊗ 𝜒𝐷 of a fixed elliptic curve 𝐸/F𝑞 (𝑡), whose 𝐿-function is denoted by 𝐿(𝑠, 𝐸 ⊗ 𝜒𝐷). A lower bound for the number of polynomials 𝐷 ∈ H∗ 2𝑔+1 such that 𝐿 URI: http://hdl.handle.net/123456789/5532 Files in this item: 1
Disertacija_nikola_lelas.pdf ( 2.523Mb ) -
Mitrinović, Dragoslav (Beograd , 1933)[more][less]
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Marovac, Ulfeta (Beograd , 2015)[more][less]
Abstract: Proteins are signi cant biological macromolecules of polymeric nature (polypeptides), which contain amino acids and are basic structural units of each cell. Their contents include 20+3 amino acids and, as a consequence, they are presented in biological databases as sequences formed from 23 di erent characters. Proteins can be classi ed based on their primary structure, secondary structure, function etc. One of possible classi cations of proteins by their function is related to their contents in a certain cluster of ortholologous groups (COGs). This classi cation is based on the previous comparison of proteins by their similarities in their primary structures, which is most often a result of homology, i.e. their mutual (evolutionary) origin. COG database is obtained by comparison of the known and predicted proteins encoded in the completely sequenced prokaryotic (archaea and bacteria) genomes and their classi cation by orthology. The proteins are classi ed in 25 categories which can be ordered in three basic functional groups (the proteins responsible for: (1) information storage and processing; (2) cellular processes and signaling; and (3) metabolism), or in a group of poorly characterized proteins. Classi cation of proteins by their contents in certain COG category (euKaryote Orthologous Groups- KOG for eukaryotic organisms) is signi cant for better understanding of biological processes and various pathological conditions in people and other organisms. The dissertation proposed the model for classi cation of proteins in COG categories based on amino acid n-grams (sequences of n- length). The set of data contains protein sequences of genomes from 8 di erent taxonomic classes [TKL97] of bacteria (Aqui cales, Bacteroidia, Chlamydiales, Chlorobia, Chloro exia, Cytophagia, Deinococci, Prochlorales), which are known to have been classi ed by COG categories. The new method is presented, based on the generalized systems of Boolean equations, used for separation of n-grams characteristic for proteins of corresponding COG categories. The presented method signi cantly reduces the number of processed n-grams in comparison to previously used methods of n-gram analysis, iv thus more memory space is provided and less time for protein procession is necessary. The previously known methods for classi cation of proteins by functional categories compared each new protein (whose function had to be determined) to the set of all proteins which had already been classi ed by functions in order to determine the group which contained most similar proteins to the one which was to be classi ed. In relation to the previous, the advantage of the new method is in its avoidance of sequence-sequence comparison and in search for those patterns (n-grams, up to 10 long) in a protein which are characteristic of the corresponding COG category. The selected patterns are added to a corresponding COG category and describe sequences of certain length, which have previously appeared in that COG category only, not in the proteins of other COG categories. On the basis of the proposed method, the predictor for determination of the corresponding COG category for a new protein is implemented. Minimal precision of the prediction is one of the predictors arguments. During the test phase the constructed predictor shown excellent results, with maximal precision of 99% reached for some proteins. According to its properties and relatively simple construction, the proposed method can be applied in similar domains where the solution of problem is based on n-gram sequence analysis. URI: http://hdl.handle.net/123456789/4308 Files in this item: 1
phdUlfetaMarovac.pdf ( 7.954Mb ) -
Stalevski, T. Marko (Belgrade, Gent , 2012)[more][less]
URI: http://hdl.handle.net/123456789/2487 Files in this item: 1
Marko_Stalevski_doktorska_disertacija.pdf ( 6.024Mb ) -
Jaćimović, Milojica (Belgrade)[more][less]
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Alimpić, Branka (Belgrade)[more][less]
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Prešić, Marica (Belgrade)[more][less]
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Popović, Georgije (Belgrade)[more][less]
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Krstev, Cvetana (Beograd , 1997)[more][less]
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Kubičela, Aleksandar (Belgrade , 1973)[more][less]
URI: http://hdl.handle.net/123456789/120 Files in this item: 1
phdAleksandarKubicela.pdf ( 30.99Mb ) -
Marinković, Silvana (Kragujevac, Serbia , 2011)[more][less]
Abstract: In this dissertation functions and equations in some classes of lattices such as Post algebras, Stone algebras and multiple-valued logics, are studied. The dissertation, beside Preface and References with 46 items, consists of five chapters. In Introduction some basic notations which will be used in next chapters are given. Main results on Boolean functions and equations are exposed in Chapter 2. In Chapter 3, assuming that a general solution is known, the class of reproductive general solutions of the equation in Stone algebra is described. All general solutions of equations in one variable in multiple-valued logic are described in Chapter 4. A necessary and sufficient conditions that given sequence of recurrent inequalities represents solution of some consistent Post equation are given in Chapter 5. Also, it is proved that every Post transformation is the parametric solution of some consistent Post equation. URI: http://hdl.handle.net/123456789/1842 Files in this item: 1
SilvanaMarinkovicDoktorat.pdf ( 360.3Kb ) -
Drašković, Zoran (Beograd , 1990)[more][less]
Abstract: U radu to da bude upotrebljena Galerkinova procedura za dobijanje jednatina polja tanke ljuske neuniformne debljine iz jednatina polja trodimenzionog kontinuuma. Tako to (s obzirom na to da je u [54], odnosno u (57] vet bilo reti o konstitutivnim jednacinama tanke ljuske) da bude zaokruien rad na razvoju tzv. meAovitog modela u teoriji tanke ljuske - to je model tri polja, koji predstavlja neklasidan pristup u metodi konadnih elemenata i odlikuje se nezavisnim aproksimiranjem polja pomeranja, polja deformacije i polja napona, a u cilju uzimanja u obzir i granidnih uslova na licima ljuske (tto je inade nemogute u klasidnoj metodi konadnih elemenata). Osnovna odlika pristupa u radu bite koriiCenje invarijantnih (tj. nezavisnih od izbora koordinatnog sistema) aproksimacija (i to Leiandrovim polinomima) tih polja, Itode mann koji je nov u literaturi, a treba da omoguei, s jedne strane, geometrijski doslednije, a, sa druge strane, jednostavnije dobijanje jednadina polja tanke ljuske iz trodimenzione teorije URI: http://hdl.handle.net/123456789/4092 Files in this item: 1
Jerdnacine_polja.PDF ( 1.204Mb ) -
Draškovic, Zoran (Belgrade , 1990)[more][less]
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Stipanić, Ernest (Belgrade)[more][less]