Mathematics
Recent Submissions
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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 phi-function 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 A-precompact (i.e. it is ε-close 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 well-known 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 ) -
Manojlović, Vesna (Beograd , 2008)[more][less]