Browsing Mathematics by Title
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Vukomanović, Đorđe (Belgrade , 1985)[more][less]
Abstract: The thesis consists of three chapters. In Chapter 1 non-strict deductive implicative algebras are studied. Weak deductive, n-deductive and ω-deductive implicative algebras are introduced. Two kinds of complements, pseudo-complement and contraposition complement in deductive implicative algebras are defined, and the connection between these algebras and deductive implicative algebras with complement are presented. Certain properties of several implicative filters in implicative algebras and their connections with homomorphsms and congruences of these algebras are studied. In the last part of Chapter 1 the representation theorems for implicative algebras mentioned in the previous parts of the chapter are proved. The strict deductive implicative algebras and their properties, which are analogous to the properties algebras from the first chapter, are studied in Chapter 2. In the last part of that chapter the representation theorems for the strict implicative algebras are proved. In Chapter 3 deductive implicative algebras in the context of deductive (sub)nets are studied. Important notions of different forms of limited distribution and many interesting connections between these distributions and the properties of deductive nets are presented. It is shown that an implicative algebra can be drowned isomorphicaly into finite deductive subnet of sets or a net such that the implication are preserved. URI: http://hdl.handle.net/123456789/40 Files in this item: 1
phdDjordjeVukomanovic.pdf ( 6.744Mb ) -
Vujošević, Biljana (Beograd , 2015)[more][less]
Abstract: In this doctoral dissertation we de ne the index of product systems of Hilbert B B modules over a unital C -algebra B. In detail, we prove that the set of all uniformly continuous units on a product system over a C -algebra B can be endowed with a structure of left-right Hilbert B B module after identifying similar units by the suitable equivalence relation and we use that construction to de ne the index of a given product system. We prove that such de ned index is a covariant functor from the category of continuous product systems to the category of two-sided BB modules. We prove that the index is subadditive with respect to the outer tensor product of product systems and we, also, prove additional properties of the index of product system that can be embedded into a spatial one (a product system that contains a central unital unit). We prove that such de ned index is a generalization of earlier de ned indices by Arveson (in the case B = C) and Skeide (in the case of spatial product systems). We, also, de ne the index of product systems in a di erent way and prove that the new de nition is equivalent to the previous one. Actually, it corresponds to Arveson's original de nition of the index. URI: http://hdl.handle.net/123456789/4235 Files in this item: 1
phdBiljanaVujosevic.pdf ( 14.03Mb ) -
Jovanović, Božidar (Beograd , 1999)[more][less]
URI: http://hdl.handle.net/123456789/4130 Files in this item: 1
Integrabilni_neholonomni.PDF ( 1.700Mb ) -
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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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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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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Krstev, Cvetana (Beograd , 1997)[more][less]
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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 ) -
Stipanić, Ernest (Belgrade)[more][less]
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Dacić, Rade (Belgrade , 1965)[more][less]
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Mitrović, Slobodanka (Belgrade)[more][less]
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Lipkovski, Aleksandar (Belgrade , 1985)[more][less]
URI: http://hdl.handle.net/123456789/25 Files in this item: 1
phdAleksandarLipkovski.pdf ( 2.471Mb ) -
Miličić, Miloš (Belgrade , 1982)[more][less]
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Malinović, Todor (Novi Sad , 1986)[more][less]