Auflistung Mathematics nach Titel
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Bejtullahu, Rasim (Pristina , 1976)[more][less]
URI: http://hdl.handle.net/123456789/80 Dateien zu dieser Ressource: 1
phdRasimBejtullahu.pdf ( 5.229Mb ) -
Delić, Aleksandra (Beograd , 2016)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
ADelicDisertacija.pdf ( 1.356Mb ) -
Zougdani, Hassan (Belgrade , 1984)[more][less]
URI: http://hdl.handle.net/123456789/148 Dateien zu dieser Ressource: 1
phdHassanKhalifaZougdani.pdf ( 4.157Mb ) -
Ćirić, Dušan (Belgrade , 1981)[more][less]
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Zejnullahu, Ramadan (Priština)[more][less]
URI: http://hdl.handle.net/123456789/164 Dateien zu dieser Ressource: 1
phdRamadanZejnullahu.pdf ( 1.723Mb ) -
Pevac, Irena (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/46 Dateien zu dieser Ressource: 1
phdIrenaPevac.pdf ( 4.513Mb ) -
Bertolino, Milorad (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/266 Dateien zu dieser Ressource: 1
phdMBertolino.pdf ( 8.733Mb ) -
Dajović, Vojin (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/174 Dateien zu dieser Ressource: 1
phdVojinDajovic.pdf ( 1.100Mb ) -
Hajduković, Dimitrije (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/38 Dateien zu dieser Ressource: 1
phdDimitrijeHajdukovic.pdf ( 1.535Mb ) -
Mališić, Jovan (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/334 Dateien zu dieser Ressource: 1
phdJovanMalisic.pdf ( 2.352Mb ) -
Jovalekić, Milica (Beograd , 2022)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
MilicaJovalekicDisertacija.pdf ( 1.796Mb ) -
Zlatanović, Milan (Niš , 2010)[more][less]
URI: http://hdl.handle.net/123456789/3812 Dateien zu dieser Ressource: 1
2011_03_14_zm.pdf ( 842.9Kb ) -
Milošević, Stefan (Beograd , 2017)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
Stefan_Milosevic_Disertacija.pdf ( 2.544Mb ) -
Kurepa, Đuro (Paris , 1935)[more][less]
Zusammenfassung: This thesis is the first systematic study of trees and ramified partially ordered sets and of their close relationship to linear orderings. It was the source of many crucial notions and problems in this area as, for example, the notions of Aronszajn and Souslin tree. The problem whether inaccessible cardinals have the tree property i. e., whether they satisfy the analogue of Koning’s infinity lemma is considered in this thesis for the first time. The thesis consists of Chapter I (the subchapters t1-t8), Chapter II (the subchapters t9-t12), and an appendix ("Complément"). In t8A11 trees are classified as "large", "étrioit" and "ambigu" according to their heights and widths. In the Theorem 5bis the following property is presented: the very thin and tall trees ("étrioit") always have cofinal branches i.e., chains intersecting every level. This result was a source of the problem whether the same fact is true about the class of slightly wider trees ("ambigu") i.e., the trees of height equal to some cardinal Θ and whose levels are now only assumed to be of size less than Θ. This is the problem known today as the problem whether Θ has the tree property. In t10.2 the important notion σE is defined, where E is a linearly (or partially) ordered set. Namely, σE is a tree of all nonempty bounded and well-ordered subsets of E with the end-extension as the tree ordering. The problem whether inaccessible cardinals have the tree property appeared in t10.3. In t10.4 two following problems are mentioned: whether every Aronszajn tree is a subtree of σQ, and if every two uniformly branching Aronszajn trees are isomorphic. A question related to previous one, whether there is a homogeneous Aronszajn tree is also mentioned. The property that every two countable infinitely branching trees of the same height are isomorphic is proved in t10.5 (Theorem 1). Appendix contains a proof that Souslin’s problem is equivalent to the statement that every uncountable tree contains an uncountable chain or untichain i.e., that three are no Souslin trees. URI: http://hdl.handle.net/123456789/326 Dateien zu dieser Ressource: 1
disert.pdf ( 7.243Mb ) -
Šovljanski, Mirjana (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/159 Dateien zu dieser Ressource: 1
phdMirjanaSovljanski.pdf ( 2.835Mb ) -
Petrić, Zoran (Belgrade)[more][less]
Zusammenfassung: In this dissertation methods of the proof theory are used to investigate coherence in some categories. Moreover, it is shown what the categorical notion of coherence means in the categorial proof theory. The thesis consists of three chapters. MacLane’s results for monoidal categories and symmetric monoidal categories are extended in Chapter 1 of the dissertation to some other categories with multiplication: relevant categories, affine categories and symmetric monoidal categories. All the results are formulated in terms of natural transformations equipped with “grafs” (g-natural transformations). It is proved, as consequences of these results, that relevant categories, affine categories and symmetric monoidal categories have the coherence property. Moreover, using these results, some basic relations between the free categories of these classes of categories are presented in Chapter 2 of the dissertation. In Chapter 3, an extension of the notion of dinatural transfomation is introduced in order to give a criterion of preservation of dinaturality under composition. An example of an application is given by proving that all cartesian closed canonical categories transformations are dinatural. Finally, an alternative sequent system for a fragment of intuitionistic propositional logic is introduced as a device, and a cut-elimination procedure is established for this system. URI: http://hdl.handle.net/123456789/187 Dateien zu dieser Ressource: 1
phdZoranPetric.pdf ( 3.130Mb ) -
Rakočević, Vladimir (Belgrade , 1984)[more][less]
URI: http://hdl.handle.net/123456789/250 Dateien zu dieser Ressource: 1
phdVladimirRakocevic.PDF ( 4.651Mb ) -
Martinović, Miroslav (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/191 Dateien zu dieser Ressource: 1
phdMiroslavMartinovic.pdf ( 3.650Mb ) -
Berić, Mladen (Belgrade , 1912)[more][less]
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Daoub, Hamza (Beograd , 2013)[more][less]
Zusammenfassung: In this thesis, we are going to highligth two di erent relations between graphs and nite commutative rings. The rst one is the well known as Unitary Cayley Graph, where the study of this assocciation and some results are presented from [1]. The second one is a completely di erent; it connects digraphs with quadratic polynomials with coe tents in Zn under the mapping (a; b) 7! (a + b; ab), for some n < 1. A Computer calculations are involved to support the study. The algorithm which is used for these calculations is built on original Mathematica and Matlab Softwares. Furthermore, Some principles are needed in this thesis for the seek of support and completeness. . . URI: http://hdl.handle.net/123456789/4267 Dateien zu dieser Ressource: 1
phdHamza_Daoub.pdf ( 1.154Mb )