Doctoral Dissertations
Collections in this community
Recent Submissions
-
Zekić, Mladen (Beograd , 2021)[more][less]
Abstract: Central place in this thesis occupy the coherence results for certain types of closed categories. Coherence results in category theory usually serve to provide a simple decision procedure for equality of arrows in some category. The approach to coherence that we follow here implies the existence of a faithfull functor from a freely generated category A of certain type to the category B in which an equality of arrows can be easily checked. Category B, which is of the same type as A, usually represents formalisation of some graphical language. Besides coherence, the second most important notion we consider in this thesis is the biproduct. The notion of biproduct in a category incorporates notions of coproduct and product. The main results in this thesis are coherence theorems for three types of closed categories with biproducts – symmetric monoidal closed categories with biproducts, com- pact closed categories with biproducts and dagger compact closed categories with dagger biproducts. Further, we present a new proof of the well-known Kelly-Mac Lane coherence theorem for symmetric monoidal closed categories. The methods we use in that proof are completely proof-theoretical, and one of the key elements in it is the cut-elimination theorem. In all the above coherence results, the graphical language is based on the category of one-dimensional cobordisms. Finaly, we give certain criteria for existence of biproducts in monoidal categories. In this regard, we rely on recent research that characterizes certain type of monoidal categories with finite biproducts by using the existence of right duals of some distinguished objects. Our criteria are a generalization of this result. URI: http://hdl.handle.net/123456789/5797 Files in this item: 1
Disertacija_13693.pdf ( 1.018Mb ) -
Mutavdžić, Nikola (Beograd , 2023)[more][less]
Abstract: In this PhD thesis we investigate bounds of the gradient of harmonic and harmonic quasiconformal mappings. We also discuss such bounds for functions that are har- monic with respect to the hyperbolic metric or certain other metrics. This research has been motivated by some recent results about Lipschitz-continuity of quasiconformal map- pings that satisfy the Laplace gradient inequality. More precisely, the mappings we consider are solutions of the Dirichlet problem for the Poisson equation and can be considered as a generalization of harmonic mappings. Besides the ball, we also work with general domains on which solutions of the Dirichlet problem are defined, as well as general codomains. Finally, we announce new results that have been formulated for regions of C1,α-smoothness, both as the domain and the codomain. Besides presenting the main results, we give an overview of general notions from differential geometry and recall some of the properties of hyperbolic metric in an n-dimensional ball. We also state properties of harmonic and sub-harmonic functions with respect to the hyperbolic metric, which are analogous to some classical results from the theory if harmonic functions and Hardy’s theory. It turns out that the gradients of hyperbolic harmonic functions behave differently from those of euclidean harmonic functions. A similar conclusion is obtained for the family of Tα-harmonic functions. Namely, unlike the space of harmonic functions, the solution of the Dirichlet problem in the space of Tα-harmonic functions is shown to be Lipschitz-continuous when so is the boundary function. In addition, we investigate Hölder- continuity of the solution of the Dirichlet problem for the Poisson equation in the euclidean and hyperbolic metric. We will present versions of the Schwarz lemma on the boundary for pluriharmonic map- pings in Hilbert and Banach spaces. These results will follow from the version of the Schwarz lemma for harmonic mappings from the unit disc to the interval (−1, 1) without the assump- tion that the point z = 0 maps to itself. Furthermore, we show a version of the boundary Schwarz lemma for harmonic mappings from a ball to a ball, not necessarily of the same dimension. The proof uses a version of the Schwarz lemma for multivariable functions, first considered by Burget. This result is obtained by integrating the Poisson kernel over so-called polar caps. The assumption that point z = 0 maps to itself is again not needed, thus yielding a generalization of a recent result by D. Kalaj. At the end of this section, it is demonstrated that the analogous result is false in the case of hyperbolic harmonic functions. In a certain sense, this means that the Hopf lemma is not valid for hyperbolic harmonic functions. Amongst various versions of the Schwarz lemma, we have been investigating bounds of the modulus for classes of holomorphic functions f on the unit disc whose index If fulfils cer- tain geometric conditions. These classes are a generalization of the star and α-star functions, previously investigated by B. N. Örnek. Our method is based on using Jack’s lemma and can be applied in certain more general cases. As an illustration, we derive the sharp bounds for the modulus of a holomorphic function f with index If whose codomain is a vertical strip, as well as bounds for the modulus of the derivative of f at point z = 0. Moreover, we give a bound for the rate of growth of the modulus of holomorphic functions on disk U that map point z = 0 to itself and whose codomain is a vertical strip. URI: http://hdl.handle.net/123456789/5796 Files in this item: 1
Disertacija_15612.pdf ( 914.6Kb ) -
Pavlović, Mrina (Beograd , 2022)[more][less]
Abstract: The studyofgalaxiesthroughhighredshiftsarekeytounderstandingthe evolutionofgalaxiesthroughcosmictimes.Assuchobjectsareverydifficultto observedirectly,theyaremainlyexaminedusingempiricallyderivedtoolssuchas the numerouscorrelationsbetweentheirdifferentparametriccharacteristics,one of thembeingthelinearrelationshipbetweenfar-infraredandradioemissionin star-forming galaxies,namedtheFarInfrared-Radio(FIR)Correlation.Although the correlationwasconsideredtobestableintermsoflinearity,recentworks, whichincludegalaxiesathighredshifts(0 < z< 6), showedalargedeviation from thecorrelationinthesesystems.Thegoalofthisdoctoraldissertationis an examinationofthephysicalprocessesthatleadtothiskindofbehavior.As a possiblecauseofthisevolution,wewillassumeforthefirsttime,andexamine interactionsbetweengalaxies(collisionsandcloseapproaches).Interactionsbe- tweengalaxiesleadtotheformationofshockwavesonlargescalesthatcanlead to changesintherelationshipbetweeninfraredandradioemissions.Ourhypoth- esis wastestedinseveralstadiumsandthemainresultsareasfollows:1.We developedmodelsoftheevolutionoftheFIRcorrelationwithredshiftasfunctions of thegalaxyinteractionrate.Wetestedthemodelsonasampleofgalaxieswith an alreadydeterminedmorphologyseparatelyfordiscgalaxiesandforgalaxies that haverecentlybeenorarecurrentlyinteracting-irregulargalaxies. 2. Inasmallsampleof34galaxiesthatwetookfrompaperMiettinenetal.(2017), it wasshownthatthereisanindicationthattheinteractionbetweengalaxiescan beresponsiblefortheevolutionofthecorrelationwiththeredshift. 3. Thenextanalysiswasperformedonamuchlargersampleofstar-forming galaxies takenfromCOSMOSfield,wherewedidnotfindanyevolutionofcorre- lation withtheredshift.Also,itwasshownthatthemeanvalueofthecorrelation parameter islowerinirregulargalaxiesthanindiskgalaxies. Although recentobservationsindicatedanevolutionoftheFIRcorrelation with redshift,theresultsofthisresearchfailedtoreproducethatevolutionand showedthattheFIRcorrelationisstablewithredshift.However,itwasalso shownthatduetotheinteractionofgalaxies,theevolutionoftheFIRcorrelation is possibleiftherepresentationofinteractingsystemsinthesampleishigher. URI: http://hdl.handle.net/123456789/5795 Files in this item: 1
Disertacija_15613.pdf ( 8.624Mb ) -
Veljković, Aleksandar (Beograd , 2023)[more][less]
Abstract: Bioinformatics as a science of the future faces the problems of processing a large amount of data that is increasing every day. In addition to the problem of data storage, the challenge is also data analysis and the understanding of hidden relations between biological entities that are observed only after unifying data from different data sources. This thesis proposes a novel data model for the unification of heterogeneous data from multiple bioinformatics databases and a system architecture design for implementing software systems based on the proposed data model. Additionally, the thesis defines an automated pipeline for discovering new semantic similarity relations based on data mining methods using the data found in the proposed data model. The data model, software architecture, and automatic pipeline are evaluated using data from five real-world bioinformatics databases. The results demonstrate a high flexibility of the data model and the high efficiency of the software system implemented following the proposed architecture design. URI: http://hdl.handle.net/123456789/5794 Files in this item: 1
Disertacija_15649.pdf ( 2.864Mb ) -
Racković Babić, Kristina (Beograd , 2022)[more][less]
Abstract: Interplanetary dust grains contain important information about the Solar System. Analyzing these particles is an important aspect of the heliosphere study. Dust impacts have been observed using radio and wave instruments onboard the spacecraft since the 1980s. The interaction between the impact-generated plasma cloud and antenna – spacecraft system elements generates the characteristic signal waveform. The present work focuses on the detection and interpretation of the dust generated signals from radio instruments onboard various spacecraft orbiting at 1 AU. In the first part of the thesis, we aim to develop a model which links the observed electric signals to the dust impact properties.We propose a new model which takes into account the effect of impact - ionization - charge collection and electrostatic-influence. Our model provides an analytical expression for the pulse. It allows us to measure the amount of total ion charge, the fraction of escaping charge, the rise timescale, and the relaxation timescale. The proposed model is simple and convenient for large data fitting. To validate the model, we use the Time Domain Sampler (TDS) subsystem of the STEREO/WAVES instrument, which generates high-cadence time series of voltage pulses for each monopole. Since the beginning of the STEREO mission in 2007, we have collected all the dust events detected by S/WAVES/TDS simultaneously on all three monopoles at 1 AU. Our study confirms that the rise time vastly exceeds the spacecraft’s short timescale of electron collection by the spacecraft. Aside from electron dynamics, we also obtained interesting results regarding the cloud’s electron temperature. The presented model provides an effective tool for analyzing vii dust waveforms, and is applicable for different space missions which investigate the distribution of dust particles, e.g., Solar Orbiter and Parker Solar Probe. In the second part of the thesis, we focus on the interstellar dust (ISD). Interplanetary and interstellar dust are the two main dust populations at 1 AU. Our objective is to search for interstellar dust by analyzing the data sets collected by STEREO and Wind, starting from the beginning of the missions. Between 2007 and 2012, while being at the solar minimum with a solar dipole pointing southward, all three spacecraft recorded ISD flux at 1 AU. However, before and after that period, the disappearance of the interstellar component was noticeable. The observed change of the impact rate suggests that the flux of interstellar dust at 1 AU varies with the solar cycle. Each time the magnetic dipole field changes its polarity during the solar cycle, small interstellar grains experience focusing or defocusing. Consequently, the dust grains are systematically deflected either towards, or away from the solar magnetic equator plane by the solar wind magnetic field which thus affects the dust dynamics and the total interstellar dust flux in the inner heliosphere. Our study provides the first quantitative description of the time variation of ISD flux at 1 AU. URI: http://hdl.handle.net/123456789/5793 Files in this item: 1
Disertacija_15665.pdf ( 11.11Mb )