Auflistung Mathematics nach Titel
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Đorić, Miloš (Beograd , 2022)[more][less]
Zusammenfassung: In this dissertation, the classification of some important classes od hypersurfaces M of the nearly Kähler S3 × S3 is considered, along with the parametrisation of the geodesic lines of this manifold. This manifold is one of only four examples of homogeneous, 6-dimensional, nearly Kähler manifolds. In addition to the almost complex structure J, this manifold is en- dowed with an almost product structure P , which anticommutes with J. Owing to these facts, there are two families of interesting tangent vector fields on S3 × S3, called P−singular vector fields, having similar properties as A−singular vector fields on complex quadrics Q, which are already known. The notion of P−principal and P−isotropic tangent vector fields of S3 × S3 is defined, along with their basic properties. In the case of P−principal normal vector field ξ of the hypersurface M , the partial classification is given, while the immersion of the hypersurfaces M with P−isotropic normal vector field ξ is stated explicitly. URI: http://hdl.handle.net/123456789/5324 Dateien zu dieser Ressource: 1
MilosDjoricDoktorat.pdf ( 800.8Kb ) -
Šukilović, Tijana (Beograd , 2015)[more][less]
Zusammenfassung: In the present work we classify left invariant metrics of arbitrary signature on four-dimensional nilpotent Lie groups. Their geometry is extensively studied with special emphasis on holonomy groups and decomposability of metrics. Also, isometry groups are completely described and we give examples of metrics where strict inequalities Isplit < Iaut < I hold. It is interesting that Walker metrics appear as the underlying structure of neutral signature metrics on the nilpotent Lie groups with degenerate center. We nd necessary and su cient condition for them to locally admit nilpotent group of isometries. Finally, we solve the problem of projectively equivalent metric on four-dimensional nilpotent Lie groups by showing that left invariant metric is either geometrically rigid or have projectively equivalent metrics that are also a nely equivalent. All a nely equivalent metrics are left invariant, while their signature may change. URI: http://hdl.handle.net/123456789/4453 Dateien zu dieser Ressource: 1
Doktorska_disertacija_-_Tijana_Sukilovic.pdf ( 1.501Mb ) -
Đorić, Mirjana (Beograd , 1994)[more][less]
Zusammenfassung: It is an interesting problem to study the geometry of Riemannian manifolds by investigating the propetries of geometric objects on them. It turns out that the features of the geometry of a family of geometric objects on a Riemannian manifold strongly influence the geometry of the ambient space. In this paper we focus on the same kind of problems considering the extrinsic and intrinsic geometry of tubes about geodesics on Kahler and Sasakian manifolds. In order to obtain our results we mainly work with Jacobi vector fields because this falls among the best ways of analysing the geometry of normal and tubular neighborhoods. In Chapter II we compute the explicit formulas for the shape operator of tubes about co-geodesics on Sasakian space forms, using the technique of Jacobi vector fields. Further, in Chapter III we characterize locally Hermitian symmetric spaces and complex space forms considering the shape operator and the Ricci operator of tubes about geodesics on Kahler manifolds. Finally, in Chapter IV we characterize Sasakian space forms and locally co-symmetric spaces by analysing the action of the shape operator and the Ricci operator on tubes about cp-geodesics on Sa URI: http://hdl.handle.net/123456789/4091 Dateien zu dieser Ressource: 1
Geometrija_geodezijskih.PDF ( 1.664Mb ) -
Pavlović, Miroslav (Belgrade , 1983)[more][less]
URI: http://hdl.handle.net/123456789/67 Dateien zu dieser Ressource: 1
phdMiroslavPavlovic.pdf ( 2.717Mb ) -
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 ) -
Grujić, Jelena (Beograd , 2015)[more][less]
Zusammenfassung: Despite its theoretical beauty and many phenomenological evidences, general relativity is not a complete theory and should be modi ed. Namely, under rather general conditions, general relativity yields cosmological solutions with zero size of the universe at its beginning, what means an in nite matter density. In order to solve this problem we consider nonlocal modi cation of general relativity. In particular, we analyze two nonlocal models and present their nonsingular bounce cosmological solutions for the cosmic scale factor. URI: http://hdl.handle.net/123456789/4314 Dateien zu dieser Ressource: 1
Grujic_Jelena.pdf ( 1.783Mb ) -
Rašajski, Borivoje (None)[more][less]
URI: http://hdl.handle.net/123456789/138 Dateien zu dieser Ressource: 1
phdBorivojeRasajski.pdf ( 4.982Mb ) -
Vujanović, Božidar (None)[more][less]
URI: http://hdl.handle.net/123456789/139 Dateien zu dieser Ressource: 1
phdBozidarDVujanovic.pdf ( 989.8Kb ) -
Perović, Miodrag (Belgrade)[more][less]
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Miloradović, Slobodan (Belgrade , 1982)[more][less]
URI: http://hdl.handle.net/123456789/87 Dateien zu dieser Ressource: 1
phdSlobodanMiloradovic.pdf ( 1.641Mb ) -
Pavićević, Žarko (Belgrade , 1983)[more][less]
URI: http://hdl.handle.net/123456789/259 Dateien zu dieser Ressource: 1
phdZarkoPavicevic.pdf ( 6.275Mb ) -
Glavaš, Lenka (Beograd , 2015)[more][less]
Zusammenfassung: The subject of this doctoral dissertation is related to the problems of extreme values in strictly stationary random sequences. It belongs to the topical area of probability and statistics, broadly applicable to real life situations and in many scienti c elds. It relies on large number of seminal articles and monographs. The main aim of the dissertation is to determine the asymptotic behavior of maxima of some incomplete samples from the rst-order auto-regressive processes with uniform marginal distributions. The dissertation consists of three chapters. New results (the theoretical ones and the results of computer simulations) are presented in the third chapter. Two types of the uniform ARp1q process pXnqnPN are considered: positively correlated and negatively correlated process, with the lag one correlation p1q : CorrpXn 1;Xnq equal to 1 r and 1 r , respectively, where r ¥ 2 is the parameter of the underlying process. Let pcnqnPN be a non-random 0 1 sequence, such that lim nÑ8 1 n n ¸j 1 cj p P r0; 1s. This sequence of degenerate random variables is introduced with the purpose to correspond to the sequence pXnq in the following sense: r.v. Xj is observed if cj 1, otherwise r.v. Xj is not observed (missing observation). Let us use the notation: the r.v. Mn : max 1¤j¤n Xj is maximum of the complete (size n) sample from the random sequence pXnq, and the r.v. Mn is what is called partial maximum, i.e. the maximal element of incomplete sample tXj : cj 1; 1 ¤ j ¤ nu. Based on di erent, speci c deterministic sequences pcnq it is proved that the limiting distribution, as n Ñ 8, of the two-dimensional random vector Mn;Mn , is not uniquely determined by the limit value p. This appears as a consequence of the fact that for the uniform ARp1q process one of the weak dependence conditions does not apply. Namely, the uniform ARp1q process does not satisfy the local condition under which clustering of extremes is restricted. As a consequence of this property, some interesting conclusions about asymptotic joint distributions of random variables Mn and Mn are reached. In the cases when the partial maximum Mn is determined by an arbitrary point process there are presented results obtained by simulations. The rst two chapters are rather informative. Having in mind interest in studying the asymptotic behavior of linearly standardized two-dimensional component-wise maxima the role of the rst chapter is to anticipate the concept of multivariate extreme values. In the second chapter the basic terms in the time series analysis are formulated, with the accent on the linear stationary models, especially on rst-order auto-regressive models. The special attention is dedicated to the uniform ARp1q processes, their properties and existing results concerning their extremal behavior. Still open questions are mentioned in the conclusion, in the very end of the third chapter. URI: http://hdl.handle.net/123456789/4454 Dateien zu dieser Ressource: 1
Doktorska_disertacija_Lenka_Glavas.pdf ( 1.195Mb ) -
Despotović, Radivoje (Novi Sad , 1983)[more][less]
URI: http://hdl.handle.net/123456789/18 Dateien zu dieser Ressource: 1
phdRadivojeDespotovic.pdf ( 11.88Mb ) -
Roslavcev, Maja (Beograd , 2021)[more][less]
Zusammenfassung: n this thesis we deal with the existence of Gröbner bases for finitely generated ide- als in rings of polynomials over some classes of rings which are not Noetherian. The theory of Gröbner bases is highly developed when we observe the ring of polynomials over a field or over a Noetherian ring. The case when the base ring is non-Noetherian is less examined. In that sense, the rings which will be of interest here are valuation rings of Krull dimension zero, valuation domains of Krull dimension one, also the generalization of the last: Prüfer domains of Krull dimension one. Von Neumann regular commutative rings and (p − 1)-nil-clean commutative rings will also be a matter of discussion. The conclusions of the thesis can be applied to Bezout and Boolean rings, as these form the subclasses of Prüfer and von Neumann regular rings, respectively. The thesis is mostly focused on rings of polynomials with one indeterminate. URI: http://hdl.handle.net/123456789/5245 Dateien zu dieser Ressource: 1
MRoslavcev_TEZA.pdf ( 3.044Mb ) -
Radovanović, Marko (Beograd , 2015)[more][less]
Zusammenfassung: By Borel's description, integral and mod 2 cohomology of ag manifolds is a polynomial algebra modulo a well-known ideal. In this doctoral dissertation, Gr obner bases for these ideals are obtained in the case of complex and real Grassmann manifolds, and real ag manifolds F(1; : : : ; 1; 2; : : : ; 2; k; n). In the case of Grassmann manifolds, Gr obner bases are applied in the study of Z- cohomology of complex Grassmann manifolds. It is well-known that, besides Borel's description, this cohomology can be characterized in terms of Schubert classes. By establishing a connection between this description and Gr obner bases that we obtained, a new recurrence formula that can be used for calculating (all) Kostka numbers is derived. Using the same method for the small quantum cohomology of Grassmann manifolds (instead of the classical), these formulas are improved. In the case of real ag manifolds F(1; : : : ; 1; 2; : : : ; 2; k; n), Gr obner bases are used to obtain new results on the immersions and embeddings of these manifolds, and for the calculation of the cup-length of some manifolds of this type. URI: http://hdl.handle.net/123456789/4298 Dateien zu dieser Ressource: 1
phdRadovanovic_Marko.pdf ( 1.476Mb ) -
Bokan, Neda (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/354 Dateien zu dieser Ressource: 1
phdNedaBokan.pdf ( 2.511Mb ) -
Knežević, Miljan (Beograd , 2014)[more][less]
Zusammenfassung: This thesis considers various properties of Euclidean harmonic mappings, quasiconformal mappings and generalized harmonic mappings, which are harmonic with respect to the conformal metric on the image surface. In particular, we obtained the answers to many questions concerning these classes of functions and that are related to the determination of different properties that are of essential importance for validity of the results such as those that generalize famous inequalities of the Schwarz-Pick type. The approach used was geometrical in nature, via analyzing the properties of the Gaussian curvature of the conformal metrics we are dealing with. URI: http://hdl.handle.net/123456789/4280 Dateien zu dieser Ressource: 1
phdKNEZEVIC_MILJAN.pdf ( 1.312Mb ) -
Vrećica, Siniša (Belgrade , 1984)[more][less]
URI: http://hdl.handle.net/123456789/170 Dateien zu dieser Ressource: 1
phdSinisaVrecica.pdf ( 2.835Mb ) -
Grujić, Vladimir (Belgrade)[more][less]
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Alqifiary, Qusuay Hatim Eghaar (Beograd , 2015)[more][less]
Zusammenfassung: This thesis has been written under the supervision of my mentor Prof. dr. Julka Knezevi c-Miljanovi c at the University of Belgrade in the academic year 2014-2015. The aim of this study is to investigate Hyers-Ulam stability of some types of differential equations, and to study a generalized Hyers-Ulam stability and as well as a special case of the Hyers-Ulam stability problem, which is called the superstability. Therefore, when there is a differential equation, we answer the three main questions: 1- Does this equation have Hyers -Ulam stability? 2- What are the conditions under which the differential equation has stability ? 3- What is a Hyers-Ulam constant of the differential equation? The thesis is divided into three chapters. Chapter 1 is divided into 3 sections. In this chapter, we introduce some sufficient conditions under which each solution of the linear differential equation u′′(t) + ( 1 + (t) ) u(t) = 0 is bounded. Apart from this we prove the Hyers-Ulam stability of it and the nonlinear differential equations of the form u′′(t) + F(t; u(t)) = 0, by using the Gronwall lemma and we prove the Hyers-Ulam stability of the second-order linear differential equations with boundary conditions. In addition to that we establish the superstability of linear differential equations of second-order and higher order with continuous coefficients and with constant coefficients, respectively. Chapter 2 is divided into 2 sections. In this chapter, by using the Laplace transform method, we prove that the linear differential equation of the nth-order y(n)(t) + nΣ1 k=0 ky(k)(t) = f(t) has the generalized Hyers-Ulam stability. And we prove also the Hyers-Ulam- Rassias stability of the second-order linear differential equations with initial and boundary conditions, as well as linear differential equations of higher order in the form of y(n)(x) + (x)y(x) = 0, with initial conditions. Furthermore, we establish the generalized superstability of differential equations of nth-order with initial conditions and investigate the generalized superstability of differential equations of second-order in the form of y′′(x)+p(x)y′(x)+q(x)y(x) = 0. Chapter 3 is divided into 2 sections. In this chapter, by applying the xed point alternative method, we give a necessary and sufficient condition in order that the rst order linear Alqi ary Abstract ii system of differential equations z_(t) + A(t)z(t) + B(t) = 0 has the Hyers-Ulam- Rassias stability and nd Hyers-Ulam stability constant under those conditions. In addition to that, we apply this result to a second-order differential equation y (t) + f(t)y_(t) + g(t)y(t) + h(t) = 0. Also, we apply it to differential equations with constant coefficient in the same sense of proofs. And we give a sufficient condition in order that the rst order nonlinear system of differential equations has Hyers-Ulam stability and Hyers-Ulam-Rassias stability. In addition, we present the relation between practical stability and Hyers-Ulam stability and also Hyers- Ulam-Rassias stability. URI: http://hdl.handle.net/123456789/4295 Dateien zu dieser Ressource: 1
phdQusuayAlqifiary.pdf ( 259.8Kb )