Mathematical Institute
Automatons and formal languages: descriptional and computational complexity
Automaty a formálne jazyky: popisná a výpočtová zložitosť
Effective Jacobi algorithms for EVD/SVD matrix decompositions and their numerical properties
Efektívne Jacobiho algoritmy pre EVD/SVD rozklady matíc a ich numerické vlastnosti
Efficient computation methods for nanoscale material characterization
Efektívne výpočtové metódy pre charakterizáciu materiálov v nanomierke
Chromatic Problems and Polynomials
Chromatické problémy a polynómy
Duration: |
1.1.2022 - 31.12.2025 |
Program: |
VEGA |
Project leader: |
RNDr. Kochol Martin PhD., DSc. |
Annotation: | Chromatic problems on graphs lie at the heart of graph theory, a discipline on the border of discrete mathematics,
combinatorial optimization and computer science. These problems are important for understanding structure of
graphs and complexity of discrete algorithms By its study are used cycles in graphs, linear algebra, groups,
optimization and other techniques. Nowhere-zero flows in graphs present a dual form for graph coloring
problems. The numbers of colorings and nowhere-zero flows in graphs are evaluated by chromatic and flow
polynomials, respectively. The aim of the project is to study various problems related to graph colorings. We plan
to study interpretations of the Tutte polynomials and relations among them. We plan to introduce and study
polynomials evaluating nonhomogenous variants of nowhere-zero flows on graphs and plan to study colorings of
hypergraphs. |
Classification using ensembles of neural networks
Klasifikácia ansámblami z neurónových sietí
Designing quantum higher order structures
Navrhovanie kvantových štruktúr vyššieho rádu
Ontological representation for security of information systems
Ontologická reprezentácia pre bezpečnosť informačných systémov
Advanced mathematical and statistical methods for measument and metrology
Pokročilé matematické a štatistické metódy pre meranie a metrológiu
Advanced approaches to data aggregation and applications
Pokročilé prístupy k agregácii dát a ich aplikácie
Duration: |
1.1.2023 - 31.12.2026 |
Program: |
VEGA |
Project leader: |
Mgr. Zemánková Andrea DrSc. |
Annotation: | Project is devoted to the basic research in the aggregation theory and to applications of aggregation functions in different domains. In particular, we aim to discuss construction methods and properties of aggregation on domains which generalize real intervals, such as bounded posets or lattices. To cover the need for aggregation methods for data where no natural order relation is present we plan to study betweenness-based aggregation functions. A deep study of aggregation of structures, such as orderings or strings, is also planned. Following requirements from applied domains, we plan to introduce and study several new modifications of the standard monotonicity and some other properties and discuss related types of functions. We will continue in development of recently introduced results on copulas, integrals, and from other domains. In collaboration with our foreign partners, we will focus on applications of our results in decision problems, image processing, statistical modelling, and other areas. |
Probabilistic, Algebraic and Quantum Mechanical Methods of Uncertainty Determination
Pravdepodobnostné, algebrické a kvantovo-mechanické metódy určovania neurčitosti
Duration: |
1.7.2021 - 30.6.2025 |
Program: |
SRDA |
Project leader: |
prof. RNDr. Dvurečenskij Anatolij DrSc. |
Annotation: | Using the latest methods of quantum structures we study mathematical foundations of quantum mechanics and of
quantum measurements. We deepen our knowledge about partial and total algebras like effect algebras, MValgebras,
synaptic algebras, orthomodular lattices, BL-algebras, EMV-algebras, wEMV-algebras, residuated
lattices and their non-commutative generalizations and states on them with respect to partially ordered groups.
Methods of the theory of categories clarify specific properties of quantum structures. Aggregation methods we will
be used to combine selected values of measurements into one aggregation function. Uncertainty contained in
quantum measurements will be analyze from the point of view of states, quantum channels will be aimed at
quantum mechanics, quantum information theory and for description of measures of non-compatibilities. |
Number theory and its applications
Teória čísel a jej aplikácie
Topological structures and spaces of functions
Topologické štruktúry a priestory funkcií
-
Topologické štruktúry na priestoroch funkcií
Multivalued models of uncertainty
Viachodnotové modely neurčitosti
Influence of materials on acoustic properties of historical single-manual pipe organs in Slovakia
Vplyv materiálov na akustické vlastnosti historických jendomanuálových orgánov na území Slovenska
Exceptional structures in discrete mathematics
Výnimočné štruktúry v diskrétnej matematike
Research the possibility of digital transformation of continuous transport systems
Výskum možnosti digitálnej transformácie kontinuálnych dopravných systémov
The total number of projects: 17