Mathematical Institute
Automata 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
Fuzzy Implication Functions and Their Applications
Funkcie fuzzy implikácií a ich aplikácie
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
Qualitative Theory of Dynamic Equations on Time Scales
Kvalitatívna teória dynamických rovníc na časových škálach
Qualitative properties and oscillations of differential equations and dynamical systems
Kvalitatívne vlastnosti a oscilácie diferenciálnych rovníc a dynamických systémov
| Duration: |
1.1.2024 - 31.12.2027 |
| Program: |
VEGA |
| Project leader: |
prof. RNDr. Fečkan Michal DrSc. |
| Annotation: | During the project, the following topics will be treated:
Study of differential equations (DEs) with integer- and fractional-order derivative and multiple delays, investigation of the stability and asymptotic properties of their solutions.
Existence of solutions and bifurcations of fractionally-perturbed DEs with discontinuous righ side.
Existence of bounded, chaotic or periodic solutions of DEs with non-smooth nonlinearities.
Uniqueness of a solution of functional DEs of non-integer order.
Ulam-Hyers stability of solutions of boundary value problems for fractional DEs.
Solvability of nonlinear symmetric functional-differential equations.
Applications of results to physical models.
Study of linear DEs with quaternions.
Qualitative properties of functional DEs. |
Mathematical Models of Linguistic Laws
Matematické modely zákonov lingvistiky
Modeling of Non-Classical Events and Uncertainty
Modelovanie neklasických javov a neurčitosti
Designing quantum higher order structures
Navrhovanie kvantových štruktúr vyššieho rádu
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Nové perspektívy a aplikácie vo výskume agregačných funkcií
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. |
Theoretical properties and applications of special families of probability distributions
Teoretické vlastnosti a aplikácie špeciálnych tried rozdelení pravdepodobnostiti
Number theory and its applications
Teória čísel a jej aplikácie
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 Descrete Mathematics: Properties, Constructions and Classifications
Výnimočné štruktúry v diskrétnej matematike: vlastnosti, konštrukcie a ich klasifikácie
Research the possibility of digital transformation of continuous transport systems
Výskum možnosti digitálnej transformácie kontinuálnych dopravných systémov
The total number of projects: 19
