Mathematical Institute
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Algebrické a topologické aspekty agregačných funkcií
Efficient computation methods for nanoscale material characterization
Efektívne výpočtové metódy pre charakterizáciu materiálov v nanomierke
Graph invariants, symmetries and labellings
Grafové invarianty, symetrie a ohodnotenia
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. |
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InoCHF – výskum a vývoj v oblasti inovatívnych technológií v manažmente pacientov s CHF
Classification using ensembles of neural networks
Klasifikácia ansámblami z neurónových sietí
Qualitative properties and bifurcations of differential equations and dynamical system
Kvalitatívne vlastnosti a bifurkácie diferenciálnych rovníc a dynamických systémov
Mathematical models of non-classical events and uncertainty
Matematické modely neklasických javov a neurčitosti
Models and algorithms for computing with incomplete information
Modely a algoritmy pre výpočty s neúplnou informáciou
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
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. |
Probability Distributions and their Applications in Modeling and Testing
Rozdelenia pravdepodobnosti a ich aplikácie v modelovaní a testovaní
Topological structures and spaces of functions
Topologické štruktúry a priestory funkcií
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Topologické štruktúry na priestoroch funkcií
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
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Využitie konceptu digitálneho dvojčaťa v manažmente zdravotného stavu rizikových skupín tehotných žien
The total number of projects: 18
