Mathematical Sciences
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Vučetić, Milica (Beograd , 2017)[more][less]
Zusammenfassung: In this dissertation we discuss in uence of H emission from supernova remnants (SNRs) on H derived star formation rates (SFRs). We present the detection of 16 optical SNR candidates in a part of nearby spiral galaxy IC342, and two more poten- tial SNRs in NGC 185 galaxy. The candidates were detected by applying [S ii]/H ratio criterion on observations made with the 2 m telescope at Rozhen National Astronomical Observatory in Bulgaria. Also, in this dissertation we present the most up-to-date list of nearby galaxies with optically detected SNRs. When deri- ving H star formation rates, assumption is that the radiation is coming from the ionized gas surrounding hot and young stars { Hii regions. In this case, emission from SNRs contaminates H ux used to derive SFR. We found that the contribu- tion of SNRs' ux to the total H ux, for 18 galaxies in our sample of galaxies with optical SNRs, is 5 5%. Due to the observational selection effects, the SNR contamination of SFRs derived herein represents only a lower limit. M83 is the galaxy with the most detected optical SNRs and in this galaxy SNRs account for 9 per cent of the total H emission. We expect that fraction similar to this would be close to the real contribution of SNR emission to the total H emission in spiral galaxies. Using two dwarf galaxies as an example, Holmberg IX and NGC 185, we show that the contamination of H ux by SNRs, or other sources, can be much larger, up to ten times higher than total H ux coming from Hii regions of the observed galaxy. URI: http://hdl.handle.net/123456789/4501 Dateien zu dieser Ressource: 1
Milica_disertacija_21.03.2017.pdf ( 26.28Mb ) -
Dimitrijević, Ivan (Beograd , 2017)[more][less]
Zusammenfassung: Einstein theory of gravity successfully describes the Solar system. It also predicts the existence of the black holes, gravitational lenses and gravitational waves, which have been observed successfully. On the other hand Einstein theory of gravity is not tested on the large cosmic sccale. Therefore, we consider the nonlocal modi ed gravity and get new solutions for the cosmic scale factor a(t). Moreover we consider space-time perturbations of the de Sitter space. URI: http://hdl.handle.net/123456789/4500 Dateien zu dieser Ressource: 1
doktorska_disertacija_Dimitrijevic_Ivan.pdf ( 1.342Mb ) -
Simić, Danijela (Beograd , 2017)[more][less]
Zusammenfassung: In this thesis is presented interactive formalization of various models of geometry and algebraic methods for automated proving geometry theorems. We present our current work on formalizing analytic (Cartesian) plane geometries within the proof assistant Isabelle/HOL. We give several equivalent definitions of the Cartesian plane and show that it models synthetic plane geometries (using both Tarski’s and Hilbert’s axiom systems). We also discuss several techniques used to simplify and automate the proofs. As one of our aims is to advocate the use of proof assistants in mathematical education, our exposure tries to remain simple and close to standard textbook definitions, but completely formal and mechanically verifiable. This formalization presents the develop of the necessary infrastructure for implementing decision procedures based on analytic geometry within proof assistants. Furthermore, we investigate complex numbers. Deep connections between complex numbers and geometry had been well known and carefully studied centuries ago. Fundamental objects that are investigated are the complex plane (usually extended by a single infinite point), its objects (points, lines and circles), and groups of transformations that act on them (e.g., inversions and Möbius transformations). In this thesis we treat the geometry of complex numbers formally and present a fully mechanically verified development within the theorem prover Isabelle/HOL. We discuss different approaches to formalization and discuss major advantages of the more algebraically oriented approach. Apart from applications in formalizing mathematics and in education, this work serves as a ground for formally investigating various non-Euclidean geometries and their intimate connections. We also present a formalization of part of Tarski axiom system withing Poincare disk model in Isabelle/HOL. Further on, we analyze connections between geometry and polynomials and the use of these connections. In Euclidean geometry, objects and relations between them can be expressed as polynomials. Further, any geometry construction can be expressed by set of polynomials and geometry statements can be proved by using algebraic methods (e.g. the Gröbner bases method or Wu’s method) over that set of polynomials. We describe an implementation of an algorithm in Isabelle/HOL that accepts a term representation of a geometry construction and returns its corresponding set of polynomials. Our further work will be to use the method of Gröbner bases within the Isabelle system on the generated polynomials, in order to prove correctness of the given construction. Furthermore, we investigate how spatial geometry constructions can be presented using polynomials. We investigate two different approaches in deriving those polynomials and then compare efficiency of algebraic provers depending on the approach used. We present a fully automated system for transforming geometry constructions into set of polynomials. Our further work would be to relate these geometry provers with dynamic geometry software and thus make easier for students to use it. URI: http://hdl.handle.net/123456789/4499 Dateien zu dieser Ressource: 1
06062017danijela_doktorat.pdf ( 1.158Mb ) -
Stojanović, Milan (Beograd , 2017)[more][less]
Zusammenfassung: The goal of this dissertation is to determine values of local dynamical constants. This goal is achieved through examination of multiple samples of selected stars near the Sun. The selection is done by using planar and vertical eccentricities as sampling criteria. The solution for calculating eccentricities is given. In the next step a large sample of stars is selected by defining upper limits for eccentricities and vertical amplitude. Then nested subsamples are formed in two ways: in the first one upper eccentricity limit is subjected to decreasing, in the other one this is the case with upper amplitude of oscillations perpendicular to the plane. The values of the local dynamical constants are deduced by analysing this material. URI: http://hdl.handle.net/123456789/4498 Dateien zu dieser Ressource: 1
Stojanovic_Milan_teza.pdf ( 8.577Mb ) -
Karapetrović, Boban (Beograd , 2017)[more][less]
Zusammenfassung: In this thesis, we study the in nite Hilbert matrix viewed as an operator, called the Hilbert matrix operator and denoted by H and Libera operator, denoted by L, on the classical spaces of holomorphic functions on the unit disk in the complex plane. It is well known that the Hilbert matrix operator H is a bounded operator from the Bergman space Ap into Ap if and only if 2 < p < 1. Also, it is known that the norm of the Hilbert matrix operator H on the Bergman space Ap is equal sin 2 p , when 4 p < 1, and it was conjectured that kHkAp!Ap = sin 2 p ; when 2 < p < 4. In this thesis we prove this conjecture. We nd the lower bound for the norm of the Hilbert matrix operator H on the weighted Bergman space Ap; , kHkAp; !Ap; sin ( +2) p ; for 1 < + 2 < p: We show that if 4 2( + 2) p, then kHkAp; !Ap; = sin ( +2) p ; while in the case 2 +2 < p < 2( +2), upper bound for the norm kHkAp; !Ap; , better then known, is obtained. We prove that the Hilbert matrix operator H is bounded on the Besov spaces Hp;q; if and only if 0 < p; ; = 1 p + 1 < 1. In particular, operator H is bounded on the Bergman space Ap; if and only if 1 < + 2 < p and it is bounded on the Dirichlet space Dp = Ap; 1 if and only if maxf1; p 2g < < 2p 2. We also show that if > 2 and 0 < " 2, then the logarithmically weighted Bergman space A2 log is mapped by the Hilbert matrix operator H into the space A2 log 2" . If 2 R, then the Hilbert matrix operator H maps logarithmically weighted Bloch space Blog into Blog +1. We also prove that operator H maps logarithmically weighted Hardy-Bloch space B1 log , when 0, into B1 log 1 and that this result is sharp. Also, we have that the space VMOA is not mapped by the Hilbert matrix operator H into the Bloch space B. On the other hand, we nd that the Libera operator L is bounded on the Besov space Hp;q; if and only if 0 < p; ; = 1 p + 1. Then, we prove that if > 1, then the logarithmically weighted Bergman space A2 log is mapped by the Libera operator L into the space A2 log 1 , while if 2 R, then the Libera operator L maps logarithmically weighted Bloch space Blog into itself. If > 0, we have that operator L maps logarithmically weighted Hardy-Bloch space B1 log into B1 log 1 and we show that this result is sharp. The well known conjecture due to Korenblum about maximum principle in Bergman space Ap states: Let 0 < p < 1. Then there exists a constant 0 < c < 1 with the following property. If f and g are holomorphic functions in the unit disk D, such that jf(z)j jg(z)j for all c < jzj < 1, then kfkAp kgkAp . Hayman proved Korenblum's conjecture for p = 2 and Hinkkanen generalized this result, by proving conjecture for all 1 p < 1. The case 0 < p < 1 of conjecture still remains open. In this thesis we resolve this case of the Korenblum's conjecture, by proving that Korenblum's maximum principle in Bergman space Ap does not hold when 0 < p < 1. URI: http://hdl.handle.net/123456789/4497 Dateien zu dieser Ressource: 1
Boban_Karapetrovic_doktorska_disertacija.pdf ( 1.392Mb )