Browsing Mathematical Sciences by Title
-
Močnik - Najman (Beograd , 1909)[more][less]
-
Stajić, Vlastimir (Beograd , 1942)[more][less]
-
Stajić, Vlastimir (BEOGRAD , 1933)[more][less]
-
Stajić, Vlastimir (Beograd , 1940)[more][less]
-
Stajić, Vlastimir (Beograd , 1933)[more][less]
-
Latković, Nikola (BEOGRAD , 1935)[more][less]
-
Mihajlović, S.; Simić, M. (Beograd , 1934)[more][less]
-
Stajić, Vlastimir (BEOGRAD , 1928)[more][less]
-
Stajić, Vlastimir (Beograd , 1930)[more][less]
-
Hočevar, Franjo (Zagreb , 1919)[more][less]
URI: http://hdl.handle.net/123456789/5301 Files in this item: 1
Aritmetika_Hocevar_Varicak.pdf ( 49.03Mb ) -
Živanović, Darko (Beograd , 2011)[more][less]
URI: http://hdl.handle.net/123456789/5152 Files in this item: 1
Darko.Zivanovic.Master.Rad.pdf ( 1.308Mb ) -
Živanović, Darko (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
URI: http://hdl.handle.net/123456789/1841 Files in this item: 1
Darko.Zivanovic.Master.Rad.pdf ( 1.308Mb ) -
Moconja, Slavko (Beograd , 2015)[more][less]
Abstract: In this thesis we study asymmetric regular types. If p is regular and asymmetric over A, then there exists an order such that Morley sequences in p over A are strictly increasing. It turns out that for every small model M A, the order type of a maximal Morley sequence in p over A whose elements are from M does not depend on the choice of the sequence, i.e. it is an invariant of the model M denoted by Invp;A(M). In the countable case we can determine all possibilities for Invp;A(M): either Invp;A(M) is an arbitrary countable linear order or, provided that it contains at least two elements, it is a countable dense linear order (possibly with one or both endpoints). Also, we study the connection between Invp;A(M) and Invq;A(M), where p and q are two regular and asymmetric over A types such that p A 6?w q A. We distinguish two kinds of non-orthogonality: bounded and unbounded. Under the assumption that p and q are convex, in the bounded case we get that Invp;A(M) and Invq;A(M) are either isomorphic or anti-isomorphic, while under the assumption of strong regularity, in the unbounded case we get that Dedekind completions of Invp;A(M) and Invq;A(M) are either isomorphic or anti-isomorphic. In particular we study the following class of structures: expansions of linear orderings with countably many unary predicates and countably many equivalence relations with convex classes. We provide new examples of regular types. Namely, it turns out that every global invariant type in this context is regular, and every non-algebraic type over A has precisely two global extensions which are invariant over A. We also study the connection between the question of existence of a quasi- minimal model of a complete rst-order theory and the question of existence of a global strongly regular type. We also deal with the problem whether every quasi- minimal group must be abelian. It turns out that this question has the positive answer provided that the global extension of the generic type of a quasi-minimal group is asymmetric over ;. URI: http://hdl.handle.net/123456789/4282 Files in this item: 1
phdMoconja_Slavko.pdf ( 2.254Mb ) -
Kadelburg, Zoran (Belgrade)[more][less]
-
Milošević, Bojana (Beograd , 2016)[more][less]
Abstract: Goodness of t and symmetry tests occupy a signi cant part of nonparametric statistic. Most of classical tests are based on the distance between the assumed distribution function and its consistent estimate, empirical distribution function. The symmetry tests are analogously constructed. A new approach that is especially attractive in recent years is making tests based on characterizations of di erent types. Those tests use U-empirical distribution functions (generalized empirical ones), U-empirical transforms (eg. Laplace transform, characteristic functions etc.) and U-empirical moments of distributions. The main advantage of these tests is that they are often free of some distribution parameters. Therefore they are suitable for testing composite hypothesis. For purpose of comparison of tests the Bahadur e ciency has become very popular. One of the reasons is that it does not require the asymptotic normality of test statistics. In addition, Bahadur and Pitman e ciencies very often locally coincide. It turns out that for determining Bahadur e ciency it is necessary to nd large deviations function under null hypothesis. If that is not possible, usually the approximate Bahadur e ciency is used. It requires the existence of asymptotic distribution and the asymptotic behavior of its tail under null hypothesis, and the limit in probability under alternative distribution. The goals of the thesis are the construction of new goodness of t and symmetry tests based on U-statistics and V -statistics, deriving the asymptotic distribution of proposed statistics, their large deviation functions and Bahadur e ciencies or their approximations. The thesis is divided into two parts. The rst part consists of three chapters. In the rst chapter the theory of U-statistics and V -statistics as well as U-empirical and V -empirical distribution function and some other empirical transforms is presented. The second chapter is devoted to the U-statistics and V -statistics with estimated parameters. The third chapter deals with asymptotic e ciency of nonparametric tests. Most of the chapter is devoted to Bahadur e ciency. In the same chapter the large deviation function for a new class of tests statistics is derived. This result is presented in [69]. The second part, which starts with the fourth chapter, is dedicated to new tests based on U-statistics and V -statistics. In the fourth chapter some type of characterizations which are used within the next chapters for construction of tests are presented. They include characterizations based on equidistribution of some statistics among which the characterizations of symmetric distributions stand out, then those based on functional equations that the distribution function satis es, those based on the independence of statistics and those based on moments. Two new characterizations of symmetric distributions are also presented. The fth chapter deals with new goodness of t tests. There are four new exponentiality tests, two new goodness of t tests for a family of Pareto distribution, as well as two new goodness of t tests for logistic distribution (see [66], [69]). Also one new class of uniformity tests which can be used as goodness of t test for any predetermined continuous distribution is proposed (see [67]). The sixth chapter is devoted to new symmetry tests. Five new symmetry tests are proposed. In the seventh chapter there are new exponentiality tests based on U-statistics and V -statistics with estimated parameters. A special attention is given to new tests based on U- empirical Laplace transforms. Beside those, some tests based on U-empirical moments are also presented. For new presented tests local Bahadur and/or Pitman e ciency is calculated. In the nal chapter, a brief review of some applications in time series analysis is shown. URI: http://hdl.handle.net/123456789/4470 Files in this item: 1
BojanaMilosevic_doktorat.pdf ( 1.897Mb ) -
Kreačić, Eleonora (Beograd , 2012)[more][less]
URI: http://hdl.handle.net/123456789/4921 Files in this item: 1
Eleonora Kreacic Master Rad.pdf ( 1.041Mb ) -
Mikić, Marija (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
URI: http://hdl.handle.net/123456789/1823 Files in this item: 1
Marija Mikic-master rad.pdf ( 638.7Kb ) -
Mikić, Marija (Beograd , 2017)[more][less]
Abstract: The subject of this dissertation is the investigation of asymptotic properties of solutions for di erential equations of Emden-Fowler type and their generalizations. The eld to which this dissertation belongs is a Qualitative theory of ordinary di e- rential equations. Emden-Fowler di erential equation has the form (t u0(t))0 t u (t) = 0 ; where ; ; 2 R. With some changes of the variables, this di erential equation can be reduced to the equations y00 xay = 0 and y00 + xay = 0. Firstly, in this dissertation, the di erential equation y00 = xay ; where a; 2 R was observed. The conditions, which provide that this equation has in nitely many solutions de ned in some neighborhood of zero, were described here, both with the conditions, which guarantee the existence of in nitely many solutions with certain asymptotic behavior. Also, a complete picture of asymptotic behavior of solutions of equation along the positive parts of both axes is given. The conditions, which assure existence and unique solvability of solution of the Cauchy problem for this equation, were shown in the cases when the familiar theory can't be applied. In some cases, asymptotic formulas for solutions were obtained. The di erential equation y00 = xay ; where a 2 R i < 0 ; has also been taken into consideration. The conditions, which assure the existence of in nitely many solutions of observed equation tending to zero as x ! 0+, were obtained. The conditions, which assure the unique solvability of the Cauchy problem for generalized Emden-Fowler equation y00 = q(x)f(y(x)); lim x!0+ y(x) = 0; lim x!0+ y0(x) = ; were described, for any > 0 and functions f and q which satisfy certain conditions. The given results generalize the results both for sublinear Emden-Fowler di erential equation (i.e. case when 0 < < 1) and the case when < 0. In literature, it is very rare to nd the conditions for di erent values of the para- metar which appears in the equations of Emden-Fowler type. In this dissertation, the results for sublinear and superlinear di erential equation Emden-Fowler, as well as the case when < 0, are presented. Therefore, the story of the asymptotic be- havior of solutions of the observed equation is "almost complited". URI: http://hdl.handle.net/123456789/4655 Files in this item: 1
Marija_Mikic_disertacija_MTF.pdf ( 1.461Mb ) -
Špadijer, Dimitrije (, 2016)[more][less]
-
Knežević, Julka (Belgrade)[more][less]