Browsing Mathematics by Title

Bertolino, Milorad (Belgrade)[more][less]

Dajović, Vojin (Belgrade)[more][less]

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]

Jovalekić, Milica (Beograd , 2022)[more][less]
Abstract: Let M be a maximum and let N be a minimum of the nonnegative 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 ndimensional 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]

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 ) 
Kurepa, Đuro (Paris , 1935)[more][less]
Abstract: 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 t1t8), Chapter II (the subchapters t9t12), 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 wellordered subsets of E with the endextension 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 Files in this item: 1
disert.pdf ( 7.243Mb ) 
Šovljanski, Mirjana (Belgrade)[more][less]

Petrić, Zoran (Belgrade)[more][less]
Abstract: 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” (gnatural 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 cutelimination procedure is established for this system. URI: http://hdl.handle.net/123456789/187 Files in this item: 1
phdZoranPetric.pdf ( 3.130Mb ) 
Rakočević, Vladimir (Belgrade , 1984)[more][less]

Martinović, Miroslav (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/191 Files in this item: 1
phdMiroslavMartinovic.pdf ( 3.650Mb ) 
Berić, Mladen (Belgrade , 1912)[more][less]

Daoub, Hamza (Beograd , 2013)[more][less]
Abstract: 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 Files in this item: 1
phdHamza_Daoub.pdf ( 1.154Mb ) 
Daoub, Hamza (Belgrade , 2013)[more][less]
Abstract: In this thesis, we are doing to highlight two different relations between graphs and finite commutative rings. The first one is the well known as Unitary Cayley Graph, where the study of this association and some results are presented from (1). The second on is a completely different; it connects digraphs with quadratic polynomials with coeffitients in Zn under the mapping (a,b)> (a+b,ab), for some n<...... 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. Furthemore, Some principles are needed in this thesis for the seek of support and completeness... URI: http://hdl.handle.net/123456789/3834 Files in this item: 1
HDPhD_o.pdf ( 2.806Mb ) 
Grulović, Milan (Belgrade , 1984)[more][less]
Abstract: The thesis consists of five chapters. In the first part of Chapter 1 forcing relations for infinite logics are considered. It is shown that if in the case of infinite logic we want to extend syntactic apparatus adequately and that forcing joining stays deductive closed set which contains all logically valid formulas, then forcing joining has to formulate by "weak" formulas. In the second part of this chapter a correction of the proof of the interpolation theorem for infinite logics is presented. The result from Chapter 2 is the following: it is shown that all important properties of Robinson’s finite forcing are transmitted to nfinite forcing by corresponding "nnotions". Moreover, a construction of nfinite forcing joining by Henrard’s approximation chains is presented. The main result of Chapter 3 is that for each theory T of a language L there is an extension T' defined in the corresponding extension L' such that. Relations between a theory (the theory of dense linearly ordering with maximal and minimal elements, the theory of groups, the theory of Abelian groups, the theory of fields, full arithmetic, Peano’s arithmetic) and its corresponding nfinite forcing joins are studied in Chapter 4. Also relations between nfinite forcing joins are studied. A connection between nfinite forcing and the type theory are studied in Chapter 5, and some generalizations of the known results are given. URI: http://hdl.handle.net/123456789/56 Files in this item: 1
phdMilanGrulovic.pdf ( 2.377Mb ) 
Marić, Filip (Belgrade)[more][less]

Telebaković Onić, Sonja (Beograd , 2022)[more][less]
Abstract: n this dissertation the connection between Frobenius algebras and topological quantum field theories (TQFTs) is investigated. It is wellknown that each 2dimensional TQFT (2TQFT) corresponds to a commutative Frobenius algebra and conversely, i.e., that the category whose objects are 2TQFTs is equivalent to the category of commutative Frobe nius algebras. Every 2TQFT is completely determined by the image of 1dimensional sphere S1 and by its values on the generators of the category of 2dimensional oriented cobordisms. Relations that hold for these cobordisms correspond precisely to the axioms of a commutative Frobenius algebra. Following the pattern of the Frobenius structure assigned to the sphere S1 in this way, we examine the Frobenius structure of spheres in all other dimensions. For every d ≥ 2, the sphere Sd−1 is a commutative Frobenius object in the category of ddimensional cobordisms. We prove that there is no distinction between spheres Sd−1, for d ≥ 2, because they are all free of additional equations formulated in the language of multiplication, unit, comultiplication and counit. The only exception is the sphere S0 which is a symmetric Frobenius object but not commutative. The sphere S0 is mapped to a matrix Frobenius algebra by the Brauerian representation, which is an example of a faithful 1TQFT functor. We obtain the faithfulness result for all 1TQFTs, mapping the 0dimensional manifold, consisting of one point to a vector space of dimension at least 2. Finally, we show that the commutative Frobenius algebra QZ5 ⊗ Z(QS3), defined as the ten sor product of the group algebra and the centre of the group algebra, corresponds to the faithful 2TQFT. It means that 2dimensional cobordisms are equivalent if and only if the corresponding linear maps are equal. URI: http://hdl.handle.net/123456789/5353 Files in this item: 1
stoDisertacijaOnic.pdf ( 9.095Mb ) 
Tanović, Predrag (Montreal , 1994)[more][less]
Abstract: The thesis is a research about nonisolation properties of superstable types over finite domains in general. Two notions of nonisoltions, the notion of eventualstrong (i.e. esn) and the notion of internal are introduced. The thesis consists of three chapters. In Chapter 1 of the thesis the techniques of the stability theory which are used in Chapter 2 and Chapter 3 are overviewed. In Chapter 2 of the thesis NDFC theories are studied and the notions of dimension and U_αrank through partial orders are developed. It is proved that if the theory T is strictly stable and the the order type of rationals cannot be embedded into the fundamental order of $T$ and there is no strictly stable group interpretable in T^eq, then the theory T has continuum nonisomorphic countable models. It is noted that strongly nonisolated types can be present due to the dimensional discontinuity property. In Chapter 3 of the thesis small superstable theories are studied. In the first part of that chapter the eventualstrong and internally nonisolated types are considered, and some properties were proved. The second part of Chapter 3 contains the proof of the following theorem: if the theory T is a complete, superstable theory, the generic type of every simple group definable in T^eq is orthogonal to all NENI types and sup{U(p)pϵS(T)}≥ ω^ω holds, then the theory T has continuum nonisomorphic countable models. URI: http://hdl.handle.net/123456789/186 Files in this item: 1
phdPredragTanovic.pdf ( 2.221Mb ) 
Šehu, Isljam (Priština , 1985)[more][less]