Mathematical Institute
Automata and formal languages: descriptional and computational complexity
Automaty a formálne jazyky: popisná a výpočtová zložitosť
Cycles and edge colorings of cubic graphs
Cykly a hranové ofarbenia kubických grafov
Digital solutions to support the mental health of patients with chronic heart failure
Digitálne riešenia na podporu duševného zdravia pacientov s chronickým zlyhaním srdca
Fuzzy Implication Functions and Their Applications
Funkcie fuzzy implikácií a ich aplikácie
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
Automata models: descriptional and computational complexity
Modely automatov: popisná a výpočtová zložitosť
Designing quantum higher order structures
Navrhovanie kvantových štruktúr vyššieho rádu
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Nové perspektívy a aplikácie vo výskume agregačných funkcií
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. |
Advances in the qualitative theory of ordinary, partial and fractional differential equations
Pokroky v kvalitatívnej teórii obyčajných, parciálnych a zlomkových diferenciálnych rovníc
| Duration: |
1.3.2025 - 31.12.2028 |
| Program: |
SRDA |
| Project leader: |
Ing. Jadlovská Irena PhD. |
| Annotation: | The qualitative theory of differential equations is at the forefront of basic research in mathematical analysis, serving as the cornerstone for many advances in applied mathematics. Novel theoretical results in differential equations enable the modeling, analysis, and solution of complex problems across diverse scientific and technological fields, thereby bridging the gap between basic and applied research. The project primarily aims to contribute to the qualitative theory of ordinary, partial, and fractional differential equations (and inequalities), addressing current open problems in the field. The project success is built on close cooperation of local institutions - Mathematical Institute of the Slovak Academy of Sciences and the Department of Mathematics and Theoretical Informatics at Faculty of Electrical Engineering and Informatics TUKE with foreign universities and academies. The results of the basic research will be presented at international conferences and published in high-impacted scientific journals. The second, side objective of the project is the mathematical activation of engineering students and their systematic preparation (in the form of additional education) for conducting independent basic research in the area. |
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
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
Computing with incomplete information
Výpočty s nekompletnou informáciou
Research of metal organ pipe collections of historical pipe organs in Slovakia
Výskum kovového píšťalového fondu historických organov na Slovensku
Research the possibility of digital transformation of continuous transport systems
Výskum možnosti digitálnej transformácie kontinuálnych dopravných systémov
The total number of projects: 20
