Browsing Mathematical Sciences by Title
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Aleksić, Danijel (Beograd , 2026)[more][less]
Abstract: This dissertation addresses the problem of model specification testing in situa- tions where data are incomplete, utilizing the existing theory of non-degenerate and weakly degenerate U- and V-statistics. The first two chapters lay the theoretical groundwork by pre- senting essential concepts related to U- and V-statistics and the general mathematical frame- work of missing data analysis, which serve as the foundation for the new results developed in subsequent chapters. In Chapter 3, a novel test for assessing the missing completely at random (MCAR) assump- tion is introduced. This test demonstrates improved control of the type I error rate and supe- rior power performance compared to the main competitor across the majority of the simulated scenarios examined. Chapter 4 explores the application of Kendall’s test for independence in the presence of MCAR data. It provides both theoretical insights and simulation-based comparisons of the complete-case analysis and median imputation, pointing out their individual advantages and drawbacks. Chapter 5 focuses on testing for multivariate normality when data are incomplete. It rig- orously establishes the validity of the complete-case approach under MCAR and proposes a bootstrap method to approximate p -values when imputation is employed. Additionally, vari- ous imputation techniques are evaluated with respect to their impact on the type I error and the power of the test. Finally, Chapter 6 adapts the energy-based two-sample test to handle missing data by intro- ducing a weighted framework that makes full use of all available observations. Alongside some theoretical developments, the chapter presents two distinct bootstrap algorithms for p -value estimation under this approach. Additionally, the performance of several imputation methods is examined in this context, and appropriate bootstrap algorithm is proposed for that setting. URI: http://hdl.handle.net/123456789/5781 Files in this item: 1
DanijelAleksicPhDThesis.pdf ( 4.605Mb ) -
Lazarević, Srđan (Beograd , 2022)[more][less]
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Karamata, Jovan (Berlin , 1931)[more][less]
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Karamata, Jovan (Berlin , 1930)[more][less]
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Karamata, Jovan (BEOGRAD , 1932)[more][less]
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Milanković, Milutin (Leipzig , 1931)[more][less]
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Milanković, Milutin (, 1914)[more][less]
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Milić, Ivan (, 2014)[more][less]
Abstract: Multidimensional radiative transfer is an essential ingredient of modern ap- proach to modeling of astrophysical objects. Realistic modeling calls for the as- sumption of non-local thermodynamic equilibrium (NLTE), which, in turn requires self-consistent solution of coupled equations of radiative transfer statistical equilib- rium. This approach allows us to compute emergent spectrum from a given model of the object, which is, in principle, a necessary step in interpretation of observational results. Thanks to the high-resolution and high signal to noise observations, it is often possible to measure not only intensity of the light but also its state of po- larization. For interpretation of such observations it is necessary to solve radiative transfer problem for polarized radiation. This thesis deals with non-LTE transfer of (generally polarized) radiation in two- dimensional media. Thesis can be divided in two parts. In the first part, we present a numerical method for the formal solution of the radiative transfer equation in 2D Cartesian coordinate system. This method allows us to explicitly account for the contribution of non-local source functions to the local specific intensity, and, hence, to the local scattering integral. The knowledge of these contributions is necessary for an iterative solution of coupled equations of radiative transfer and statistical equilibrium. Based on this formal solution we introduce two novel schemes for multidimensional NLTE radiative transfer which have so far been used only in 1D geometry: symmetric Gauss-Seidel iteration and “Sweep-by-sweep” implicit lambda iteration, latter one being based on “Forth-and-back” implicit lambda iteration. Both methods utilize implicit use of the local source function and the source func- tion corrections each sweep of the computational grid (four times per iteration). “Sweep-by-sweep” implicit lambda iteration also uses the idea of iteration factors and achieves acceleration of about factor of seven with respect to the referent Ja- cobi method. Both new methods also significantly surpass both Jacobi iteration and Gauss-Seidel iteration on problems with periodic boundary conditions. Also, it turns out that “Sweep-by-sweep” implicit lambda iteration scales with grid resolu- tion better than the Jacobi iteration. The second part of the thesis deals with numerical polarized radiative transfer on 2D cylindrical grids. The method is based on the second order short characteristics for the formal solution and uses standard Jacobi iteration with Ng acceleration to solve the polarized non-LTE problem (Generalization to other iterative schemes is given in appendix A). This method allows for the self-consistent solution of coupled equations of radiative transfer and statistical equilibrium equation for a two level atom model for polarized radiation. The method employs reduced intensity basis where intensity and source function are written as six-vectors and source function does not depend on direction which allows for significant saving in memory and computing time. It is applicable for modeling of axisymmetric objects such as as- trophysical disks. The method has been tested on simple models of circumstellar and self-emitting disks. The most important conclusion of these computations is that the presence of the disk in the system introduces a significant degree of linear polarization due to the scattering processes and that one is able to model it in detail using our approach. Also, it is shown that the presence of rotation in self-emitting disks dramatically changes not only intensity, but also polarized spectral lines pro- files. Interplay of non-LTE, multidimensional effects and rotation results in very complicated line profiles which are non-trivial for interpretation. However, the main effect is that the rotation decreases the amount of Stokes Q component and, de- pending on the rotation velocity causes appearance of double-lobed U polarization profile. If these effects can be observed, this kind of modeling provides a useful tool for interpretation of the spectropolarimetric observations. URI: http://hdl.handle.net/123456789/4757 Files in this item: 1
IvanMilic_teza.pdf ( 1.075Mb ) -
Stanču, Matei Jon (Beograd , 2022)[more][less]
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Medan, Darko (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2009)[more][less]
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Popović, Nikola (Belgrade)[more][less]
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Forsajt, A. R. (Beograd , 1939)[more][less]
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Zeković, Vladimir (Beograd , 2020)[more][less]
Abstract: In the disertation, by the linear plasma theory we show that resonant electromagnetic (EM)micro-instabilities are excited by the two colliding plasmas which are interpenetrating eachother with the super-Alfv ́enic velocity, in the direction quasi-parallel to the magnetic field.The expected Rankine-Hugoniot shock conditions, naturally arise as a consequence of a highlyresonant interaction of ions with the instability. By using kinetic simulations, we find herethat such resonant instabilities appear in the linear stage, and we show how these instabilitiestrigger the shock formation during the non-linear stage.By theoretical modeling, we show how a magnetosonic soliton forms and leads to the periodicshock reformation and initiation of the return current of ions, which drives the EM upstreaminstability. We find that ions are being pre-accelerated by the upstream and shock instabilities ina mechanism that is similar to the diffusive shock acceleration (DSA). By our EM test particlesimulation runs we show that at quasi-parallel shocks, EM instabilities highly contribute toelectron pre-acceleration, leading to the formation of a power-law electron spectra through theFermi-like mechanism.By very long kinetic simulation runs, in this disertation we find that ions and electronsenter DSA in a similar number which is further applied in a model of non-linear DSA. Withinthis model, we obtain the theoretical particle spectra and we find the electron-to-proton ratioat high energies for the different Mach numbers. We show that the spectra of quasi-thermalparticles at the shock can be represented by a non-equilibriumκ-distribution. We find thatthe level of modification decreases andκ-index increases behind the shock, implying that theparticle distribution tends to become a Maxwellian. URI: http://hdl.handle.net/123456789/5094 Files in this item: 1
ZekovicVladimir.pdf ( 56.60Mb ) -
Batoćanin, Vladimir (Beograd , 2024)[more][less]
URI: http://hdl.handle.net/123456789/5732 Files in this item: 1
v1_masterVladimirBatocanin.pdf ( 3.366Mb ) -
Vujčić, Luka (Beograd , 2023)[more][less]
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Bačanin Džakula, Nebojša (Beograd , 2015)[more][less]
Abstract: Hard optimization problems that cannot be solved within acceptable computational time by deterministic mathematical methods have been successfully solved in recent years by population-based stochastic metaheuristics, among which swarm intelligence algorithms represent a prominent class. This thesis investigates improvements of the swarm intelligence metaheuristics by hybridization. During analysis of the existing swarm intelligence metaheuristics in some cases de ciencies and weaknesses in the solution space search mechanisms were observed, primarily as a consequence of the mathematical model that simulates natural process as well as inappropriate balance between intensi cation and diversi cation. The thesis examines whether existing swarm intelligence algorithms for global optimization could be improved (in the sense of obtaining better results, faster convergence, better robustness) by hybridization with other algorithms. A number of hybridized swarm intelligence metaheuristics were developed and implemented. Considering the fact that good hybrids are not created as a random combination of individual functional elements and procedures from di erent algorithms, but rather established on comprehensive analysis of the functional principles of the algorithms that are used in the process of hybridization, development of the hybrid approaches was preceded by thorough research of advantages and disadvantages of each involved algorithm in order to determine the best combination that neutralizes disadvantages of one approach by incorporating the strengths of the other. Developed hybrid approaches were veri ed by testing on standard benchmark sets for global optimization, with and without constraints, as well as on well-known practical problems. Comparative analysis with the state-of-the-art algorithms from the literature demonstrated quality of the developed hybrids and con rmed the hypothesis that swarm intelligence algorithms can be successfully improved by hybridization. URI: http://hdl.handle.net/123456789/4245 Files in this item: 1
phdBacaninNebojsa.pdf ( 3.813Mb ) -
Radovanović, Boris (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
URI: http://hdl.handle.net/123456789/1981 Files in this item: 1
Master rad - Boris Radovanovic R.pdf ( 2.234Mb ) -
Vuksanović, Vladimir (Beograd , 2023)[more][less]
URI: http://hdl.handle.net/123456789/5633 Files in this item: 1
v1_masterVladimirVuksanovic.pdf ( 651.7Kb ) -
Branković - Pavlović, Suzana (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2010)[more][less]
URI: http://hdl.handle.net/123456789/1885 Files in this item: 1
unapredjenje nastave.pdf ( 2.680Mb ) -
Miletić, Miloš (Beograd , 2012)[more][less]