http://hdl.handle.net/123456789/4 http://hdl.handle.net/123456789/5790 PROMENA V I R MAGNITUDA IZABRANIH KVAZARA I POVEZIVANJE SISTEMA GAIA SA SISTEMOM ICRF Jovanović, Miljana One of the main objectives of the Gaia mission of the European Space Agency is to construct a celestial reference frame at the wavelengths of the optical domain, Gaia CRF. This frame needs a link to the International Celestial Reference Frame – ICRF which is fixed with respect to distant objects (quasars). The objects serving for the purpose of linking are required to be visible in both domains (optical and radio). A set of 47 such objects has been proposed and included which in the radio domain have no detected extended emission. The mentioned objects are active galactic nuclei (AGN) the brightness of which varies over the whole electromagnetic spectrum. The brightness change may be due to activity in different AGN regions, but also to external factors. Such variations can lead to changes in the photocentre position and, consequently, to changes of the object coordinates. In order to establish which objects are suitable for linking these two frames we have examined the brightness variation in the optical domain. The objects have been observed from 2013 in the V and R bands. We have analysed the brightness, colour (V − R) and optical spectral index (α). It has been established that for the majority of objects the brightness is variable, or possibly variable. Almost 15% of all objects have significant changes in their brightness (more than 1 mag), only ∼10% are stable with minor brightness changes of ∼0.3 mag. The results concerning the change analysis of the colour and α are also presented. Based on these results 17 objects are chosen as suitable for linking ICRF to Gaia CRF. The results of the analysis, as well as the observed values, are essential for the examination of these objects because of their importance in astrometry, also in astrophysics. These data are relevant to a better understanding of formation and evolution of galaxies. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/123456789/5789 KOHOMOLOŠKA ALGEBRA GRASMANOVIH MNOGOSTRUKOSTI ORIJENTISANIH TRODIMENZIONALNIH RAVNI U EUKLIDSKOM PROSTORU Jovanović, Milica The analysis of Grassmann manifolds, which were first introduced in the 19th century, is one of the classical problems in the algebraic topology. When analyzing topological spaces, it is always useful to determine their cohomology algebra. The cohomology of Grassmann manifolds is already well known, but their covering spaces, so called oriented Grassmann manifolds, are far less examined. The oriented Grassmann manifold ˜Gn,k is defined to be the space of oriented k-dimensional subspaces of Rn. In this dissertation we analyze the cohomology algebra of oriented Grassmann manifolds ˜Gn,k with integer and modulo 2 coe!cients, predominantly the case k = 3. The dissertation comprises three chapters. The first chapter is an introduction where an overview of known results and necessary tools is given. In the second chapter we study the cohomology with the modulo 2 coe!cients. First of all, the known results in the case k = 2 are presented. Next, we move onto the case k = 3 where the partial description of the cohomology algebra is given. This section is based on papers published in the last several years. We give an overview of these results in the thesis, and we also present original results for n close to a power of two. In the last part of this chapter, we investigate the cohomology algebra of the manifold ˜G2t,4, and that is as far as we have come with the examination of modulo 2 cohomology. The third chapter is dedicated to the integral cohomology. This chapter, like the previous one, also splits in several sections, depending on the value of k. When k = 2, the integral cohomology is completely determined, and we present the proof for n odd. When k = 3, only the integral cohomology of ˜Gn,3, n → {6, 8, 10}, has been determined so far, while for k ↭ 4 only some partial results are known. In this segment we also analyze the connection between the integer and the modulo 2 cohomology algebra of these Grassmannians by analyzing the morphism between them induced by the modulo 2 reduction. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/123456789/5787 Hermitske strukture i geodezijske linije na četvorodimenzionalnim hiperboličkim prostorima Babić, Marijana The only non-compact four-dimensional rank-one symmetric spaces are the complex hyperbolic plane CH2 and the four-dimensional real hyperbolic space RH4. As connected homogeneous manifolds of negative sectional curvature, these spaces admit the structure of a four-dimensional real solvable Lie group equipped with a left-invariant metric. This Lie group appears naturally in the Poincar´e half-space model of real hyperbolic space and in the Siegel paraboloid model of the complex hyperbolic plane. The boundary of the paraboloid model carries the structure of the Heisenberg group. Hermitian structures consist of a left-invariant Riemannian metric together with a compatible complex structure. In this thesis, all such structures are classified and their geometric properties are studied. It is shown that every Riemannian metric on real hyperbolic space admits a two-dimensional sphere of Hermitian complex structures. In the case of the complex hyperbolic plane, some metrics admit exactly four distinct Hermitian complex structures, while others admit a two-dimensional sphere of such structures. Their curvature properties, holonomy groups, and self-duality are investigated. It is shown that the standard metric on the complex hyperbolic plane is the unique K¨ahler metric within the obtained classification, whereas all Riemannian metrics on real hyperbolic space are Einstein. Geodesics on the solvable Lie groups of the spaces CH2 and RH4, with respect to all possible left-invariant Riemannian metrics, are studied in this thesis using the Euler–Arnold equations. These equations effectively reduce a system of secondorder differential equations on a Lie group to a system of first-order equations on the corresponding Lie algebra. Numerical solutions of these equations enable the visualization of geodesics and geodesic spheres. Fri, 01 May 2026 00:00:00 GMT http://hdl.handle.net/123456789/5786 DIRECT DATA-SNAPSHOTTING AND SNAPSHOT SHARING ACROSS CLOUD-NATIVE APPLICATIONS Ristović, Ivan Cloud-computing platforms provide services to consumers through multiple serviceoffering models. Recent advances in these models have led to the emergence of serverless computing, or simply serverless, where infrastructure is managed by the service provider. Serverless is usually coupled with function-based programming model in which software systems are composed of reusable, lightweight units of code executed within isolated sandboxed environments. Major cloud-computing platforms, including Amazon Web Services (AWS), Microsoft Azure, and Google Cloud, report that a substantial proportion of their customers employ serverless solutions. Most cloud-computing providers employ a pay-as-you-go billing model. Inefficient utilization of computing resources, particularly CPU time and working memory, which constitute the most costly resources, leads to increased overall operational costs. Moreover, the requirement for resource isolation adversely affects initialization latency and results in additional CPU and working-memory overhead. Serverless sandboxes are typically deployed on top of heavyweight virtualization stacks that includeJava, JavaScript, or Python runtime environments with accompanying frameworks, further increasing working-memory consumption. Modern cloud-computing architectures use Checkpoint/Restore (abbr. c/r) techniques to freeze initialized sandboxes into a continuable form. Such techniques, in combination with cloud-native deployments, allow the virtualized environment to optimize resource consumption and share code and pre-initialized data across multiple sandboxes. However, such solutions either operate at application-build time to support data pre-initialization or sharing, or operate at execution time with limited sharing potential for data available during application execution. Such data is processed multiple times and duplicated in each sandbox. This dissertation presents Doss, a direct object snapshotting and sharing system that performs data c/r during application execution. Doss persists data directly, without transformations, into reusable and shareable snapshots. Direct snapshotting allows Doss to achieve near-constant data deserialization time, greatly improving initialization times and reducing CPU usage. Doss architecture enables snapshot sharing across application instances, eliminating the excess memory footprint associated with data re-processing and duplication. GraalDoss, a Doss implementation for Java, is integrated into the GraalVM ecosystem. GraalDoss is evaluated using 106 correctness and robustness tests and a novel set of cloudnative micro and macro benchmarks that exercise real-world scenarios. A comprehensive evaluation of GraalDoss shows a consistent near-constant data-deserialization overhead with serialization times comparable to state-of-the-art Java JSON and binary serialization libraries. GraalDoss reduces the memory footprint of web API microservice caches by sharing populated cache snapshots across microservice instances, improving the overall density by 41% for 8 microservice instances and improving first-response times by 34%. In NLP applications, GraalDoss improves the pipeline execution times by six orders of magnitude by snapshotting pipeline results and subsequently loading the snapshots. Wed, 01 Apr 2026 00:00:00 GMT