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MEASURING BLACK HOLE MASSES IN ACTIVE GALACTIC NUCLEI USING THE POLARIZATION OF BROAD EMISSION LINESSavić, Đorđe (Beograd , 2019)[more][less]
Abstract: Supermassive black holes (SMBHs) reside in the heart of nearly every massive galaxy in the Universe. Most of them lie dormant, but when the nearby gas is abundant, it will enter an active phase and form an active galactic nucleus (AGN). In their active phase, SMBHs have a profound effect on the host galaxy evolution and its environment. Reliable SMBH mass measuring is therefore an important task in modern astronomy. For that purpose, a method has been recently proposed by Afanasiev & Popović (2015) that uses the rotation of the polarization plane position angle across the broad emission line profile in order to trace the Keplerian motion and determine the SMBH mass. This method assumes that broad lines are emitted from a flattened disklike region undergoing Keplerian motion, while the polarization is mainly due to the light scattering of the inner side of the coplanar dusty torus – the equatorial scattering. The goal of the thesis is to theoretically explore the possibilities of this method. We performed numerous Monte Carlo simulations for modeling equatorial scattering in AGNs using the radiative transfer code stokes (Goosmann & Gaskell 2007). We included complex motion of the emitting region in the form of radial inflows, vertical outflows, or due to the presence of the supermassive binary black holes (SMBBHs). We also selected fourwell known AGNs for observations: NGC4051, NGC4151, 3C273 and PG0844+349. Spectropolarimetry was done with the 6m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Science (SAO RAS) with the focal reducer SCORPIO. We modeled each of these AGNs using observational data available from the literature, and we compared the results of our models with observational data. We find that this method can be used as a new independent way to measure the SMBH masses in AGNs. The influence of the inflows and the outflows can be ignored if they are much lower than the Keplerian velocity. Additionally, when the scattering region is close to the broad line region, this method becomes independent of the viewing inclination. For SMBBHs, this method cannot be used, however, we obtained unique polarization profiles which are not common for a single SMBH, which could be used for identifying possible SMBBH candidates. SMBH mass estimates for the four observed AGNs are in good agreement with the masses obtained using other methods, such as the method of reverberation mapping. Method for independent SMBH mass measurements has been theoretically and experimentally verified in this work, which is very important for the future research that is dealing with the SMBH influence on its immediate environment. URI: http://hdl.handle.net/123456789/4821 Files in this item: 1
teza_Djordje_Savic.pdf ( 13.41Mb ) 
Algali, Khola (Beograd , 2019)[more][less]
Abstract: In this thesis we give some new asymptotic formulas for mean values of multiplicative functions of several variables depending on GCD and LCM of arguments. We obtain an asymptotic formula with a power saving error term for the summation function of a family of generalized least common multiple and greatest common divisor functions of several integer variables. Xn 1,...,nk+`≤x [n1,...,nk]a (n1,...,nk)c , [nk+1,...,nk+`]b (nk+1,...,nk+`)d = Ck,a,c;`,b,d (a + 1)k(b + 1)` xk(a+1)+`(b+1) + O xk(a+1)+`(b+1)−1 2+ and Xn 1,...,nk+`≤x [n1,...,nk]a (n1,...,nk)c , [nk+1,...,nk+`]b (nk+1,...,nk+`)d (n1 ...nk)a(nk+1 ...nk+`)b = Ck,a,c;`,b,d xk+` + O xk+`−1 2+ . Also we obtain an asymptotic formula with a power saving error term for the summation function of Euler phifunction evaluated at iterated and generalized least common multiples of four integer variables. Xn 1,n2,n3,n4≤x ϕ [n1,n2]a (n1,n2)c , [n3,n4]b (n3,n4)d = Ca,c;b,d (a + 1)2(b + 1)2 x2a+2b+4 + O x2a+2b+7 2+ . URI: http://hdl.handle.net/123456789/4820 Files in this item: 1
khola_phd_new_ver.pdf ( 665.4Kb ) 
Lazović, Zlatko (Beograd , 2019)[more][less]
Abstract: In the ﬁrst section we present the theory on uniform spaces and measures of noncompactness in metric and uniform spaces. Next, we recall the basic concepts and properties of C∗ and W∗algebras and Hilbert modules over these algebras with some known topologies on Hilbert W∗module. In the second section we construct a local convex topology on the standard Hilbert module l2(A), such that any compact” operator (i.e., any operator in the norm closure of the linear span of the operators of the form maps bounded sets into totally bounded sets. In the biginning A presents unital W∗algebra, leter on A presents unital C∗algebra. The converse is true in the special case where A = B(H) is the full algebra of all bounded linear operators on a Hilbert space H. In the third section we deﬁne a measure of noncompactness λ on the standard Hilbert C∗module l2(A) over a unital C∗algebra, such that λ(E) = 0 if and only if E is Aprecompact (i.e. it is εclose to a ﬁnitely generated projective submodule for any ε > 0) and derive its properties. Further, we consider the known, Kuratowski, Hausdorﬀ and Istratescu measure of noncompactnes on l2(A) regarded as a locally convex space with respect to a suitable topology. We obtain their properties as well as some relationships between them and above introduced measure of noncompactness. In the forth section we generalize the notion of a Fredholm operator to an arbitrary C∗algebra. Namely, we deﬁne ﬁnite type elements in an axiomatic way, and also we deﬁne a Fredholm type element a as such an element of a given C∗algebra for which there are ﬁnite type elements p and q such that (1−q)a(1−p) is invertible. We derive an index theorem for such operators. In subsection Corollaries we show that many wellknown operators are special cases of our theory. Those include: classical Fredholm operators on a Hilbert space, Fredholm operators in the sense of Breuer, Atiyah and Singer on a properly inﬁnite von Neumann algebra, and Fredholm operators on Hilbert C∗modules over a unital C∗algebra in the sense of Mishchenko and Fomenko. URI: http://hdl.handle.net/123456789/4819 Files in this item: 1
dr_Zlatko_Lazovic.pdf ( 2.019Mb ) 
Timotijević, Marinko (Beograd , 2019)[more][less]
URI: http://hdl.handle.net/123456789/4818 Files in this item: 1
Disertacija_Marinko_Timotijevic.pdf ( 1.189Mb ) 
Danić, Dimitrije (, 1885)[more][less]
Abstract: Tema Danićeve disertacije su konformna preslikavanja eliptičkog paraboloida na ravan, prateći definicije i formalizam koje je uveo Gaus (F. Gauss) za tu vrstu preslikavanja. U tom razmatranju izveo je određene parcijalne diferencijalne jednačine koje takođe analizira i rešava. Njegov doprinos bile su metode u rešavanju kompleksnih eliptičkih integrala, uvođenju eliptičkih transformacija i primeni eliptičkih funkcija u rešavanju ovih parcijalnih jednačina. URI: http://hdl.handle.net/123456789/4796 Files in this item: 3
DDanic_thesis_documentation.pdf ( 239.6Kb )DDanic_thesis_transl_SRB.pdf ( 1.764Mb )DDanic_thesis.pdf ( 1.420Mb )