Auflistung Mathematical Sciences nach Titel
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Mijović, Vuksan (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
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Algale, Khola (Beograd , 2012)[more][less]
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Telebaković Onić, Sonja (Beograd , 2022)[more][less]
Zusammenfassung: n this dissertation the connection between Frobenius algebras and topological quantum field theories (TQFTs) is investigated. It is well-known that each 2-dimensional TQFT (2-TQFT) corresponds to a commutative Frobenius algebra and conversely, i.e., that the category whose objects are 2-TQFTs is equivalent to the category of commutative Frobe- nius algebras. Every 2-TQFT is completely determined by the image of 1-dimensional sphere S1 and by its values on the generators of the category of 2-dimensional 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 d-dimensional 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 1-TQFT functor. We obtain the faithfulness result for all 1-TQFTs, mapping the 0-dimensional 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 2-TQFT. It means that 2-dimensional cobordisms are equivalent if and only if the corresponding linear maps are equal. URI: http://hdl.handle.net/123456789/5353 Dateien zu dieser Ressource: 1
stoDisertacijaOnic.pdf ( 9.095Mb ) -
Theodossiou, E.; Mantarakis, P.; Dimitrijević, M.; Manimanis, V.; Danezis, E. (Cambridge Scientifc Publishers , 2011)[more][less]
URI: http://hdl.handle.net/123456789/3295 Dateien zu dieser Ressource: 1
AAT_27_162_2011.pdf ( 164.4Kb ) -
Pavlović, Rade (Faculty of Mathematics, University of Belgrade , 2008)[more][less]
Zusammenfassung: We investigate the ful¯llment of conditions for application of Nekhoroshev theorem to real dynamical system, such as the motion of asteroids under the perturbation by major planets. We have in particular analyzed the regions of the phase space where asteroid families of Koronis and Veritas are located. The results obtained for a number of selected family members indicate that in these regions even stricter conditions (convexity, quasi-convexity and 3- jet), than the condition of steepness required by the theorem, are fullled. Consequently, the theorem of Nekhoroshev can be applied to members of Koronis family and to the members of Veritas family with regular motion. URI: http://hdl.handle.net/123456789/717 Dateien zu dieser Ressource: 1
phdRadePavlovic.pdf ( 3.135Mb ) -
Čukić, Ivan (Beograd , 2018)[more][less]
Zusammenfassung: There is a big class of problems that require software systems with asynchronously executed components. For example, distributed computations have the distributed nodes that process the data asynchronously to one anot- her, service-oriented architectures need to process separate requests asynchrono- usly, and multi-core and heterogeneous systems need to have multiple separa- te tasks running concurrently to best utilize the hardware. Even ordinary GUI applications need asynchronous components – the user interface needs to be re- sponsive at all times which means that no matter in what state the program is in, it needs to process and react to the input events coming from the user. The necessity of concurrency and asynchronous execution brings in the added com- plexity of the Inversion of Control (IoC) into the system, either through mes- sage passing or through event processing. IoC makes code difficult to develop and reason about, it increases component coupling and inhibits clean functional or object-oriented software design. In this dissertation, a method for solving the problems that IoC introduces is presented. It presents a way to model both synchronous and different types of asynchronous tasks with the continuation monad. The continuation monad serves as a primitive to build more complex control flow structures that mimic the control flow structures of the host programming language. It also allows for building more complex control structures specialized for parallelism, transactional execution, and for simulating functional programming idioms with asynchronous tasks through a generalization of the continuation monad that allows the asynchronous tasks to generate results one at a time. This allows for writing programming systems with asynchronously executed components by writing seemingly synchronous imperati- ve or functional code while leaving it up to the compiler to do all the heavy lifting and convert the written code to asynchronously executed set of tasks. Another benefit of the presented method is that it allows for easier automatic handling of the data lifetime without the need for garbage collection. This method has been successfully applied and tested in several Free/Libre Open Source Software and proprietary real-world software projects used by hun- dreds of millions of people around the world. In this dissertation, an example of a secure project management system is described which is based on a similar system implemented as a part of the KDE Plasma project. This dissertation also contains the important parts of the implementation of the AsynQt library which extends the Qt library, and its concurrency primitive – QFuture class – with functional reactive programming patterns based on the method proposed in this dissertation. URI: http://hdl.handle.net/123456789/4738 Dateien zu dieser Ressource: 1
ivan_cukic_phd.pdf ( 1.328Mb ) -
Tanović, Predrag (Montreal , 1994)[more][less]
Zusammenfassung: The thesis is a research about nonisolation properties of superstable types over finite domains in general. Two notions of nonisoltions, the notion of eventual-strong (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_α-rank 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 non-isomorphic countable models. It is noted that strongly non-isolated 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 eventual-strong 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 non-isomorphic countable models. URI: http://hdl.handle.net/123456789/186 Dateien zu dieser Ressource: 1
phdPredragTanovic.pdf ( 2.221Mb ) -
Bilimović, Anton (Beograd , 1961)[more][less]
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Milisavljević, R. Slaviša (Belgrade , 2013)[more][less]
Zusammenfassung: The problem of the minimal mutual distances for two confocal elliptical orbits (local minima), in the literature known as the proximity calculation for minor planets and recognised recently as Minimal Orbit Intersection Distance – MOID, occupies a very important place in astronomical studies, not only because of the prediction of possible collisions of asteroids and other celestial bodies, but also because of the fact that by analysing the behaviour of asteroids during their encounters it is possible to determine their masses, changes of orbital elements and other important characteristics. Dealing with this problem in this thesis the author has analysed the distance function for two elliptical confocal orbits of minor planets combining analytical and numerical methods for proximity calculation. A survey of all relevant results in this field from the middle of the XIX century till our days indicates that the problem has been transformed from looking for a solution of two transcendental equations by applying various methods and approximations of long duration towards efficient and rapid solutions of vector equations of the system which describes the problem. In the thesis a simple and efficient analytic-numerical method has been developed, presented and applied. It finds out all the minima and maxima in the distance function and, indirectly, makes it possible to determine also the inflection points. The method is essentially based on Simovljevic’s (1974) graphical interpretation and on transcendental equations developed by Lazovic (1993). The present method has been examined on almost three million pairs of real elliptical asteroid orbits and its possibilities and the computation results have been compared to the algebraic solutions given by Gronchi (2005). The case of a pair of confocal orbits with four proximities found by Gronchi (2002), who applied the method of random samples and carried out numerous simulations with different values of orbital elements, gave the motivation to try here to find out such a pair among the real pairs of asteroid orbits. Thanks to the efficacy of the method developed in the thesis two such pairs have been found and their parameters are presented. In addition to the one meantioned above a further analysis of distance function through simulations including more than 20 million different pairs of asteroid orbits has resulted in several additional interesting solutions of the distance function. The results are given in the form of tables and plots showing the diversity of solutions for the distance function. URI: http://hdl.handle.net/123456789/2490 Dateien zu dieser Ressource: 1
phdSlavisaMilisavljevic.pdf ( 3.815Mb ) -
Miletić, Nevena (Beograd , 2019)[more][less]
URI: http://hdl.handle.net/123456789/4816 Dateien zu dieser Ressource: 1
masMileticNevena.pdf ( 448.1Kb ) -
Joksimović, Dušan (Beograd , 2015)[more][less]
URI: http://hdl.handle.net/123456789/4315 Dateien zu dieser Ressource: 1
Joksimovic_Dusan.pdf ( 713.6Kb ) -
Šehu, Isljam (Priština , 1985)[more][less]
URI: http://hdl.handle.net/123456789/151 Dateien zu dieser Ressource: 1
phdIsljamASehu.pdf ( 2.582Mb ) -
Ivanović, Natalija (Beograd , 2019)[more][less]
URI: http://hdl.handle.net/123456789/4803 Dateien zu dieser Ressource: 1
masIvanovicNatalija.pdf ( 1.307Mb ) -
Popović, Nadežda (Beograd , 2019)[more][less]
URI: http://hdl.handle.net/123456789/4791 Dateien zu dieser Ressource: 1
masPopovic_Nadezda.pdf ( 8.618Mb ) -
Drešević, Milan (Beograd , 1973)[more][less]
URI: http://hdl.handle.net/123456789/4096 Dateien zu dieser Ressource: 1
Funkcionalni_prostori.PDF ( 2.559Mb ) -
Drešević, Milan (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/308 Dateien zu dieser Ressource: 1
phdMilanDresevic.pdf ( 3.667Mb ) -
Krtinić, Djordje (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
URI: http://hdl.handle.net/123456789/1825 Dateien zu dieser Ressource: 1
krtinic_disertacija.pdf ( 388.8Kb ) -
Šobot, Boris (Novi Sad , 2009)[more][less]
Zusammenfassung: The method of forcing is widely used in set theory to obtain various consistency proofs. Complete Boolean algebras play the main role in applications of forcing. Therefore it is useful to define games on Boolean algebras that characterize their properties important for the method. The most investigated game is Jech’s distributivity game, such that the first player has the winning strategy iff the algebra is not (!, 2)-distributive. We define another game characterizing the collapsing of the continuum to !, prove several sufficient conditions for the second player to have a winning strategy, and obtain a Boolean algebra on which the game is undetermined. URI: http://hdl.handle.net/123456789/297 Dateien zu dieser Ressource: 1
phdBorisSobot.pdf ( 987.6Kb ) -
Šobot, Boris (UNIVERSITY OF NOVI SAD FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS AND INFORMATICS , 2009)[more][less]
URI: http://hdl.handle.net/123456789/733 Dateien zu dieser Ressource: 1
Boris Sobot teza.pdf ( 987.6Kb ) -
Radovanović, Nina (Beograd , 2023)[more][less]
URI: http://hdl.handle.net/123456789/5586 Dateien zu dieser Ressource: 1
masterRadovanovicNina.pdf ( 1.629Mb )