Browsing Mathematical Sciences by Title
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Svetlik, Marek (Beograd , 2020)[more][less]
Abstract: In this dissertation we consider various versions of the Schwarz lemma and theSchwarz-Pick lemma for holomorphic, harmonic and harmonic quasiregular mappings. Inaddition, in order to present new results, an overview of the results that can be considered asclassical is given. As one of the most important consequence of the Schwarz-Pick lemma forholomorphic mappings, an introduction of the hyperbolic distancedΩon the simply connecteddomainsΩ C(such thatΩ6=C) is given in details, as well as the connection of that distanceand holomorphic mappings. All versions of the Schwarz lemma and the Schwarz-Pick lemma for harmonic mappingsare shown as assertions analogous to the corresponding claims for holomorphic mappings.In the proofs of these assertions, the properties of the hyperbolic distance and Euclideanproperties of hyperbolic disks are used. Firstly, we considered some versions of the Schwarzlemma for harmonic mappings from the unit disk to the interval (-1,1) and then for harmonicmappings of the unit disk into itself, without the assumption thatz= 0is mapped to itself bythe corresponding map. Thereby, the corresponding inequalities were shown to be sharp andextremal mappings were found. By using the strip and half plane method, simple proofs ofthe Schwarz-Pick lemma for real-valued harmonic mappings are given, as well as the simpleproofs of their corollaries that are formulated in terms of corresponding hyperbolic distances.For both holomorphic and harmonic mappings a version of the Schwarz lemma have beenformulated and proved in the case where the values of these mappings and values of thenorms of their differentials, at the pointz= 0, are given. Also, in that case we showed thatthe corresponding inequalities are sharp and extremal mappings were found. It has also beenshown that the same methods can be used to obtain Harnack’s inequalities for harmonicmappings, as well as for their generalizations.Furthermore, we give simple proofs of a version of the Schwarz-Pick lemma for harmonicquasiregular mappings whose codomain is a half plane or a strip. One version of the Schwarzlemma for harmonic quasiregular mappings from the unit disk into a strip is obtained thanksto the appropriate (which seems unexpected) inequality satisfied by the Euclidean and hyper-bolic distances on the strip. By using the properties of the Gaussian curvature we also showthat harmonic quasiconformal mappings of the hyperbolic domain into convex hyperbolicdomain are quasi-isometries of the corresponding metric spaces.The introduction of the hyperbolic distance is shown in two ways. The first way is classi-cal one. Starting from the hyperbolic metric on the unit disk, first we define the hyperboliclength of theC1curve and then the hyperbolic distance between two given points. Thesecond one is based on the axiomatic foundation of the absolute plane geometry. Startingfrom the theorem related to the existence and the uniqueness (up to the unit for length) ofthe distance in the absolute plane (which is in accordance with the basic geometry relations- between and congruence), we simultaneously derive the formula for that distance in twomodels of that plane. One of these models is the set of complex numbersC, observed as amodel of the Euclidean plane and the second one is the unit disk that is considered as thePoincaré disk model of hyperbolic plane. URI: http://hdl.handle.net/123456789/5091 Files in this item: 1
svetlik_marek-phd.pdf ( 1.279Mb ) -
Kocić, Ognjen (Beograd , 2015)[more][less]
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Subotić, Danijel (Beograd , 2017)[more][less]
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Kostić, Anica (Beograd , 2017)[more][less]
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Ilić, D. Ivana (Belgrade , 2013)[more][less]
Abstract: For the sequence of heavy-tailed and possibly dependent random variables with the missing observations the estimation of the tail-index is considered. Under minimal but verifiable assumption of ''extremal dependence'' we proved the consistency of geometric-type estimator (Brito and Freitas, 2003). We extended results from Mladenovic and Piterbarg (2008) and proved the consistency and the asymptotic normality of the Hill estimator. Illustrative examples are provided. URI: http://hdl.handle.net/123456789/2485 Files in this item: 1
Elektronska verzija.pdf ( 3.250Mb ) -
Suvočarev, Sofija (Beograd , 2012)[more][less]
URI: http://hdl.handle.net/123456789/2207 Files in this item: 1
OCENJIVANJE PARAMETARA.pdf ( 3.195Mb ) -
Minić, Marija (Beograd , 2015)[more][less]
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Jovanović, Milan (Beograd , 2015)[more][less]
Abstract: Early papers dealing with so-called stress-strength problems were published in the middle of the 20th century. This topic, which belongs to the reliability theory, is still very active nowadays, which can be seen through the number of published papers dealing with it - around ten each year. In this dissertation, some methods for estimation of the reliability parameter for a system with independent stress and strength are presented. Also, two new models are introduced and some estimators of the reliability parameter for each of them are derived. The dissertation is divided into four chapters. In the rst chapter, some basic terms are introduced and some examples from real life, illustrating big possibilities for application of the results from this scienti c eld, are described. Sorted based on the stress and strength distributions, a chronological overview of all research activities dealing with these topics, to the author's best knowledge, is presented. Some special func- tions, which are later used for calculations, along with their main properties are shown. The expressions for the reliability parameter for some stress and strength distributions are either derived or listed. The second chapter is devoted to different methods used for point esti- mation, as well as for interval estimation of the reliability parameter of a system. For each methods estimators of the reliability parameter for some stress and strength distributions are either derived or listed. In the third chapter, a new model is introduced. In this model, the stress has geometric, while the strength has Poisson distribution. This is one of the rst, if not the rst, appearances in the literature, where the stress and strength distributions do not belong to the same family of distributions. For this model, the reliability parameter is estimated using different methods and decision on optimal estimators for usage in practice is based on the simulations. In the fourth chapter, another model is introduced, with the stress and strength distributions which are not only from different families of distribu- tions, but also do not belong to the same type of distributions. The stress has geometric, while the strength has exponential distribution. The reliabil- ity parameter for this model is also estimated using different methods, and the decision on optimal estimators for usage in practice is once again based on the simulations. URI: http://hdl.handle.net/123456789/4352 Files in this item: 1
Jovanovic_Milan_teza.pdf ( 4.636Mb ) -
Mladenović, Pavle (Belgrade , 1985)[more][less]
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Petrić, Bojana (Beograd , 2014)[more][less]
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Reljić, Pavle (Beograd , 2019)[more][less]
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Stamenić, Anica (Beograd , 2018)[more][less]
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Nešić, Dimitrije (Belgrade , 1890)[more][less]
URI: http://hdl.handle.net/123456789/468 Files in this item: 1
book001DimitrijeNesic.pdf ( 4.238Mb ) -
Đurišić, Kosta (Beograd , 2021)[more][less]
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Sokolović, Željko (Beograd , 1987)[more][less]
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Karamata, Jovan (Akademija Prirodnih Nauka , 1926)[more][less]
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Jovanović, Milena (Beograd , 2021)[more][less]
Abstract: The subject of this thesis is a precise determination of the Baryonic Mass Func- tion (BMF) for a representative sample of nearby galaxies, where BMF stands for the distribution of the galaxies’ baryonic masses. Detailed dynamical models were derived for a sample of galaxies based on the publicly available THINGS (The HI Nearby Galaxy Survey) survey, based on the the 21 cm emission line of atomic hydrogen hi. THINGS rotation curves, that reflect dynamical mass, were fitted by the sum of the contributions from the stellar component, neutral atomic gas, and dark matter for 20 THINGS galaxies. The mass of stellar components is measured from the Spitzer photometry in the 3.6 μm band, while the amount of atomic gas is derived directly from the radio observations in THINGS. For the assumed dark matter dis- tribution we used the observationally motivated pseudo-isothermal profile (ISO) and the Navarro-Frenk-White (NFW) profile based on the ΛCDM cosmological model. Dynamical modeling of the total mass was performed with free scaling of the stellar component contribution (mass-to-light ratio, M/L), and also with the same parameter fixed on a value consistent with stellar evolution population models. Con- vergence of the fitting procedure was reached for all the dynamical models with the free mass-to-light ratio, while the modeling with the fixed ratio was successful for 16 objects. The mass of the stellar component, gas, dark matter, baryonic, and total mass, were derived for the sample of galaxies and the aforementioned four sets of dynamical models (two dark matter models with both free and fixed M/L values). The total BMF is constructed by summing the masses of the baryonic compo- nents (stars and gas) for galaxies in the given range of galactic masses. Furthermore, we discuss how typical our Galactic neighborhood and our Galaxy, the Milky Way, as a giant spiral, are in terms of component masses and their place on the global (and local) BMF. URI: http://hdl.handle.net/123456789/5244 Files in this item: 1
Doktorska_disertacija_Jovanovic_Milena.pdf ( 14.28Mb ) -
Palibrk, Marijana (Beograd , 2020)[more][less]
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Jurković, Monika (, 2019)[more][less]
Abstract: The subject of this PhD thesis are Type II Cepheids. Type II Cepheids are pulsating Population II stars with masses of around 0.5 0.6 M⊙. Their mass determines where they are positioned on the Hertzsprung-Russell diagram (HRD), that is, their luminosity and eective temperature. These stars can be found in the Milky Way, the Magellanic Clouds, and in other distant galaxies. They occupy a narrow strip on the HRD which is called the instability strip. Here the radii and luminosity change periodically, and this change can be seen in the light curves. Because of their age, and their position on the HRD, these variables form a separate period-luminosity relation (PL relation). Using the spectral energy distribution models we determined in this thesis the eective temperatures and luminosities, and from evolutionary models the masses and radii, for Type II Cepheids and anomalous Cepheids in the Large and Small Magellanic Clouds. In the thesis, the rst period- luminosity relation was constructed using bolometric magnitude (Mbol). The thesis also presents the reclassication of Type II Cepheids from the Milky Way using the Fourier decomposition of the light curves measured in V lter. The Fourier decomposition was used to calculate the Fourier parameters, which were then used to compare the stars from the Milky Way with the sample of known Type II Cepheids and anomalous Cepheids from the OGLE-III catalogue for the Large Magellanic Cloud. From the 59 stars (taken from the General Catalogue of Variable Stars), 18 turned out to be anomalous Cepheids, 1 anomalous Cepheid pulsating in the rst overtone, 11 classical Cepheids, 2 peculiar W Virginis stars or classical Cepheids, and 7 were found not to be pulsating stars at all. URI: http://hdl.handle.net/123456789/4760 Files in this item: 1
Jurkovic_Monika.dok.dis.pdf ( 15.79Mb ) -
Petrić, Jovan (Belgrade , 1960)[more][less]