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]

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]

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]

Drešević, Milan (Belgrade)[more][less]

Drešević, Milan (Beograd , 1973)[more][less]
URI: http://hdl.handle.net/123456789/4096 Files in this item: 1
Funkcionalni_prostori.PDF ( 2.559Mb )