Browsing Mathematics by Title
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Ćirić, Miroslav (Beograd , 1991)[more][less]
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Živaljević, Rade (Belgrade , 1983)[more][less]
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Vukićević, Petar (Berlin , 1894)[more][less]
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Nešović, Emilija (Kragujevac, Serbia , 2011)[more][less]
Abstract: The field of research in this dissertation is consideration of different types of curves in Minkowski spaces, as well as defining the notion of hyperbolic angle between spacelike and timelike vector. The research in this dissertation is connected with the following subjects: geometry of hyperquadrics in Minkowski space, finite type submanifolds and plane Minkowski geometry. This dissertation, beside Preface and References with 56 items, consists of four chapters: 1. Curves in hyperquadrics in Minkowski spaces; 2. Classification of 2 –type curves in Minkowski n-space ; 3. W-curves in Minkowski space-time; 4. Hyperbolic angle between vectors. In Chapter 1 the curves lying in hyperquadrics in Minkovski 3-space and Minkowski 4-space are studied. More precisely, the results related with the spacelike and timelike curves lying pseudosphere in Minkowski 3-space are presented. Also, the necessary and sufficient conditions for spacelike curves lying in pseudohyperbolic space in Minkowski 4-space are given. Curves of finite type 2 in Minkowski n-space are studied in details in Chapter 2. Also, there are given some known results related with finite type submanifolds. In Chapter 3, W-curves (i.e. the curves having constant all curvature functions) in Minkowski space-time are studied and some relations between W-curves and finite type curves are given. Finally, in Chapter 4 one of the basic notions in Lorentzian geometry is considered, i.e. hyperbolic angle between two non-null vectors. The notion of hyperbolic angle between two timelike vectors is well-known, so in this chapter it is defined the notion between spacelike and timelike vectors. The measure of hyperbolic angle is also defined. By using the notion of hyperbolic angle between spacelike and timelike vectors, all spacelike curves of constant precession with non-null principal normal and all timelike curves of constant precession in Minkowski 3-space are classified and their explicit parameter equations are given. URI: http://hdl.handle.net/123456789/1916 Files in this item: 1
Dokt. disertacija dr E. NešovićR.pdf ( 3.472Mb ) -
Pantić, Živadin (Belgrade)[more][less]
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Bojović, R. Dejan (Kragujevac, Serbia , 1999)[more][less]
Abstract: The field of research in this dissertation is consideration of convergence of finite differnce method for parabolic problems with generalized solutions. The research in this dissertation is connected with the following subjects: Numerical Analysis and Partial Differential Equations. This dissertation, beside Preface and References with 56 items, consists of five chapters: 1. Introductory Topics; 2. Parabolic Problems with Variable Operator: Convergence in W(2,1)-norm; 3. Parabolic Problems with Variable Operator: Convergence in W(1,1/2)-norm; 4. Convergence in L-2 norm; 5. Application of Interpolatyion theory In Chapter 1 a brief review of the Sobolev spaces, anisotropic Sobolev spaces, multipliers in Sobolev spaces, interpolation theory of Banach spaces and existence of generalized solution of parabolic problems are presented. Initial-boundary-value problems with variable (time-dependent) operator are considered in Chapters 2 and 3. In Chapter 2 is proved convergence of finite difference scheme in discrete W(2,1) Sobolev norm. Convergence in W(1,1/2) norm is proved in Chapter 3. In Chapter 4, parabolic problem with variable coefficients is considered and convergence in L-2 norm is proved. Finally, in Chapter 5 , interpolation theory is applied to the convergence analysis. URI: http://hdl.handle.net/123456789/1915 Files in this item: 1
doktorska disertacija Scan reduce.pdf ( 1.523Mb ) -
Hodžić, Sandra (Beograd , 2016)[more][less]
Abstract: In recent years there has been increasing interest in modeling the physical and chemical processes with equations involving fractional derivatives and integrals. One of such equations is the subdi usion equation which is obtained from the di usion equation by replacing the classical rst order time derivative by a fractional derivative of order with 0 < < 1: The subject of this dissertation is the initial-boundary value problem for the subdi usion equation and its approximation by nite di erences. At the beginning, the one-dimensional equation is observed. The existence and the uniqueness of weak solution is proved. The stability and the convergence rate estimates for implicite and the weighted scheme are obtained. The main focus is on two-dimensional subdi usion problem with Laplace operator as well as problem with general second-order partial di erential operator. It is assumed that the coe cients of the di erential operator satisfy standard ellipticity conditions that guarantees existence of solution in appropriate spaces of Sobolev type. In that case, apart from above mensoned, we constructed the additive and the factorized di erence schemes. We investigated their stability and convergence rate depending on the smoothness of the input data and of generalized solution. URI: http://hdl.handle.net/123456789/4455 Files in this item: 1
Disertacija_Sandra_Hodzic.pdf ( 913.2Kb ) -
Bejtullahu, Rasim (Pristina , 1976)[more][less]
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Delić, Aleksandra (Beograd , 2016)[more][less]
Abstract: The time fractional di usion-wave equation can be obtained from the classical diffusion or wave equation by replacing the rst or second order time derivative, respectively, by a fractional derivative of order 0 < 2. In particular, depending on the value of the parameter , we distinguish subdi usion (0 < < 1), normal di usion ( = 1), superdi usion (1 < < 2) and ballistic motion ( = 2). Fractional derivatives are non-local operators, which makes it di cult to construct e cient numerical method. The subject of this dissertation is the time fractional di usion-wave equation with coe cient which contains a singular distribution, primarily Dirac distribution, and its approximation by nite di erences. Initial-boundary value problems of this type are usually called interface problems. Solutions of such problems have discontinuities or non-smoothness across the interface, i.e. on support of Dirac distribution, making it di cult to establish convergence of the nite di erence schemes using the classical Taylor's expansion. The existence of generalized solutions of this initial-boundary value problem has been proved. Some nite di erence schemes approximating the problem are proposed and their stability and estimates for the rate of convergence compatible with the smoothness of the solution are obtained. The theoretical results are con rmed by numerical examples. URI: http://hdl.handle.net/123456789/4337 Files in this item: 1
ADelicDisertacija.pdf ( 1.356Mb ) -
Zougdani, Hassan (Belgrade , 1984)[more][less]
URI: http://hdl.handle.net/123456789/148 Files in this item: 1
phdHassanKhalifaZougdani.pdf ( 4.157Mb ) -
Ćirić, Dušan (Belgrade , 1981)[more][less]
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Zejnullahu, Ramadan (Priština)[more][less]
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Pevac, Irena (Belgrade)[more][less]
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Bertolino, Milorad (Belgrade)[more][less]
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Dajović, Vojin (Belgrade)[more][less]
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Hajduković, Dimitrije (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/38 Files in this item: 1
phdDimitrijeHajdukovic.pdf ( 1.535Mb ) -
Mališić, Jovan (Belgrade)[more][less]
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Jovalekić, Milica (Beograd , 2022)[more][less]
Abstract: Let M be a maximum and let N be a minimum of the non-negative martingale X1, X2, . . . , Xn. It is well known, that if X1 = 1, then γ(‖M ‖1) ≤ E (Xn log Xn) and γ(‖N ‖1) ≤ E (Xn log Xn) , where γ(x) = x − 1 − log x, for all x > 0. In this thesis, we prove the analogue of this result in the case when 1 < p < ∞, by proving that δp (‖M ‖p p ) ≤ ‖Xn‖p and δp (‖N ‖p p ) ≤ ‖Xn‖p, where δp(x) = ( 1 − 1 p ) x 1 p + 1 p x 1 p −1, for all x > 0. We also obtain a probabilistic proof of the fact min ρ∈D(Qn) ∫ Qn dx1 . . . dxn ρ (x1, . . . , xn)p−1 ∏n j=1 xαj +1 j = n∏ j=1 ( p p − αj − 1 )p , where p > 1, αj < p − 1 for j = 1, . . . , n and D (Qn) is family of all densities on the n-dimensional unit cube Qn = (0, 1)n in Rn. This provides the proof of the multidimensional weighted Hardy inequality. Namely, if f : Rn + → (0, ∞) is a measurable function, p > 1 and αj < p − 1 for j = 1, . . . , n, then ∫ Rn + n∏ j=1 xαj j Hnf (x)p dx ≤ n∏ j=1 ( p p − αj − 1 )p ∫ Rn + n∏ j=1 xαj j f (x)p dx, where Hnf (x) = 1 x1 . . . xn ∫ x1 0 · · · ∫ xn 0 f (t) dt, is a multidimensional Hardy operator, x = (x1, . . . , xn) ∈ Rn +, t = (t1, . . . , tn) and dt = dt1 . . . dtn. Let B(t) be a standard planar Brownian motion and r(θ) be the length of the projection of B[0, 1] on the line generated by the unit vector eθ = (cos θ, sin θ), where 0 ≤ θ ≤ π. We nd the common distribution function F of the random variables r(θ). Namely, we prove that F(x) = 8 ∞∑ n=1 ( 1 x2 + 1 (2n − 1)2π2 ) exp ( − (2n − 1)2π2 2x2 ) , for every x > 0. As immediate consequence, lower bound for the expected diameter of the set B[0, 1], better than known, is obtained. Namely, it is known that Ed ≥ 1.601, where d is the diameter of the set B[0, 1]. In this thesis we show Ed ≥ 1.856. URI: http://hdl.handle.net/123456789/5323 Files in this item: 1
MilicaJovalekicDisertacija.pdf ( 1.796Mb ) -
Zlatanović, Milan (Niš , 2010)[more][less]
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Milošević, Stefan (Beograd , 2017)[more][less]
Abstract: In this paper we present some norm inequalities for certain elementary operators and inner product type transformers, specially for Schatten norms, if the families of operators generating those transforms consists of arbitrary operators, and Q norms if at least one of those families consists of mutually commuting normal operators. Among others, we present inequalities that are generalizing the inequality p IA AX p IB B 6 X AXB ; from [11, Th. 2.3], for normal contractions and arbitrary unitarily invariant norm, to the case of Schatten norms and arbitrary contractions, as well as Q norms if at least one of the contractions A or B is normal. Also, by applying norm inequalities for operator monotone and operator convex functions, some refined Cauchy - Schwarz operator inequalities, as well as Minkowski and Landau - Gruss norm inequalities for operators are obtained as well. URI: http://hdl.handle.net/123456789/4656 Files in this item: 1
Stefan_Milosevic_Disertacija.pdf ( 2.544Mb )