Browsing Mathematics by Title

Knežević, Miljan (Beograd , 2014)[more][less]
Abstract: This thesis considers various properties of Euclidean harmonic mappings, quasiconformal mappings and generalized harmonic mappings, which are harmonic with respect to the conformal metric on the image surface. In particular, we obtained the answers to many questions concerning these classes of functions and that are related to the determination of different properties that are of essential importance for validity of the results such as those that generalize famous inequalities of the SchwarzPick type. The approach used was geometrical in nature, via analyzing the properties of the Gaussian curvature of the conformal metrics we are dealing with. URI: http://hdl.handle.net/123456789/4280 Files in this item: 1
phdKNEZEVIC_MILJAN.pdf ( 1.312Mb ) 
Vrećica, Siniša (Belgrade , 1984)[more][less]

Grujić, Vladimir (Belgrade)[more][less]

Alqifiary, Qusuay Hatim Eghaar (Beograd , 2015)[more][less]
Abstract: This thesis has been written under the supervision of my mentor Prof. dr. Julka Knezevi cMiljanovi c at the University of Belgrade in the academic year 20142015. The aim of this study is to investigate HyersUlam stability of some types of differential equations, and to study a generalized HyersUlam stability and as well as a special case of the HyersUlam stability problem, which is called the superstability. Therefore, when there is a differential equation, we answer the three main questions: 1 Does this equation have Hyers Ulam stability? 2 What are the conditions under which the differential equation has stability ? 3 What is a HyersUlam constant of the differential equation? The thesis is divided into three chapters. Chapter 1 is divided into 3 sections. In this chapter, we introduce some sufficient conditions under which each solution of the linear differential equation u′′(t) + ( 1 + (t) ) u(t) = 0 is bounded. Apart from this we prove the HyersUlam stability of it and the nonlinear differential equations of the form u′′(t) + F(t; u(t)) = 0, by using the Gronwall lemma and we prove the HyersUlam stability of the secondorder linear differential equations with boundary conditions. In addition to that we establish the superstability of linear differential equations of secondorder and higher order with continuous coefficients and with constant coefficients, respectively. Chapter 2 is divided into 2 sections. In this chapter, by using the Laplace transform method, we prove that the linear differential equation of the nthorder y(n)(t) + nΣ1 k=0 ky(k)(t) = f(t) has the generalized HyersUlam stability. And we prove also the HyersUlam Rassias stability of the secondorder linear differential equations with initial and boundary conditions, as well as linear differential equations of higher order in the form of y(n)(x) + (x)y(x) = 0, with initial conditions. Furthermore, we establish the generalized superstability of differential equations of nthorder with initial conditions and investigate the generalized superstability of differential equations of secondorder in the form of y′′(x)+p(x)y′(x)+q(x)y(x) = 0. Chapter 3 is divided into 2 sections. In this chapter, by applying the xed point alternative method, we give a necessary and sufficient condition in order that the rst order linear Alqi ary Abstract ii system of differential equations z_(t) + A(t)z(t) + B(t) = 0 has the HyersUlam Rassias stability and nd HyersUlam stability constant under those conditions. In addition to that, we apply this result to a secondorder differential equation y (t) + f(t)y_(t) + g(t)y(t) + h(t) = 0. Also, we apply it to differential equations with constant coefficient in the same sense of proofs. And we give a sufficient condition in order that the rst order nonlinear system of differential equations has HyersUlam stability and HyersUlamRassias stability. In addition, we present the relation between practical stability and HyersUlam stability and also Hyers UlamRassias stability. URI: http://hdl.handle.net/123456789/4295 Files in this item: 1
phdQusuayAlqifiary.pdf ( 259.8Kb ) 
Vukomanović, Đorđe (Belgrade , 1985)[more][less]
Abstract: The thesis consists of three chapters. In Chapter 1 nonstrict deductive implicative algebras are studied. Weak deductive, ndeductive and ωdeductive implicative algebras are introduced. Two kinds of complements, pseudocomplement 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 leftright 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 twosided 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 ) 
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 zerodivisors (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]

Pažanin, Ratomir (Belgrade , 1980)[more][less]

Mitrinović, Dragoslav (Beograd , 1933)[more][less]

Jaćimović, Milojica (Belgrade)[more][less]

Alimpić, Branka (Belgrade)[more][less]

Prešić, Marica (Belgrade)[more][less]

Krstev, Cvetana (Beograd , 1997)[more][less]

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 multiplevalued 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 multiplevalued 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]

Dacić, Rade (Belgrade , 1965)[more][less]

Mitrović, Slobodanka (Belgrade)[more][less]

Lipkovski, Aleksandar (Belgrade , 1985)[more][less]
URI: http://hdl.handle.net/123456789/25 Files in this item: 1
phdAleksandarLipkovski.pdf ( 2.471Mb )