Zaměření projektu je do oblastí s přesahem matematických disciplin, tedy algebry, geometrie, analýzy (včetně numeriky) a statistiky. Typickým úkolem je autonomní řízení, kde kromě analýzy obrazu a metod umělé inteligence vstupuje do hry i optimální řízení, rozhodovací strategie a výpočetní optimalizace. Řízení robotických ramen, zvyšování přesnosti obrábění, plánování svozu odpadu nebo řízení tavného procesu jsou další ukázky problémů řešených komplexními matematickými metodami.

Description in English
The project focuses on areas that overlap mathematical disciplines, i.e. algebra, geometry, analysis (including numerics) and statistics. A typical task is autonomous driving, where, in addition to image analysis and artificial intelligence methods, optimal control, decision-making strategies and computational optimization also come into play. Controlling robotic arms, increasing machining accuracy, waste collection planning or melting process control are other examples of problems solved by complex mathematical methods.

FSI-S-23-8161

Czech

Vašík Petr, doc. Mgr., Ph.D. - principal person responsible
Benko Matej, Ing. - fellow researcher
Byrtus Roman, Ing. - fellow researcher
Čermák Jan, prof. RNDr., CSc. - fellow researcher
Derevianko Anna, Ing., Ph.D. - fellow researcher
Druckmüller Miloslav, prof. RNDr., CSc. - fellow researcher
Eryganov Ivan, Ing., Ph.D. - fellow researcher
Fedorková Lucie, Ing., Ph.D. - fellow researcher
Franců Jan, prof. RNDr., CSc. - fellow researcher
Hrdina Jaroslav, doc. Mgr., Ph.D. - fellow researcher
Kalenská Petra, Ing., Ph.D. - fellow researcher
Kureš Miroslav, doc. RNDr., Ph.D. - fellow researcher
Loučka Pavel, Ing., Ph.D. - fellow researcher
Machovičová Tatiana, Ing. - fellow researcher
Maya Baraah - fellow researcher
Navrátil Dušan, Ing. - fellow researcher
Petrák Filip, Mgr. - fellow researcher
Šlapal Josef, prof. RNDr., CSc. - fellow researcher
Štarha Pavel, doc. Ing., Ph.D. - fellow researcher
Tomáš Jiří, doc. RNDr., Dr. - fellow researcher

Institute of Mathematics
- responsible department (1.2.2024 - not assigned)
Institute of Mathematics
- internal (1.1.2023 - 31.12.2025)
Faculty of Mechanical Engineering
- beneficiary (1.1.2023 - 31.12.2025)

WARREN, B.; KUREŠ, M. Every positive integer is a sum of at most n+2 centered n-gonal numbers. Mathematica Slovaca, 2025, vol. 75, no. 3, p. 515-524. ISSN: 1337-2211.
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ŠLAPAL, J. Adjacencies for recognition of digital Jordan surfaces. Aequationes Mathematicae, 2025, vol. 99, no. 3, p. 989-1001. ISSN: 1420-8903.
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ŠTARHA, P.: AQA_CorCap_2024; AQA Corona Capture version 2024. Ústav matematiky Fakulta strojního inženýrství Technická 2896/2 61669 Brno. URL: http://www.zam.fme.vutbr.cz/~starha/aqa_corcap/. (software)
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ČERMÁK, J.; FEDORKOVÁ, L.; NECHVÁTAL, L. Periodic solutions in a linear delay difference system. Electronic Journal of Qualitative Theory of Differential Equations, 2025, vol. 2025, no. 10, p. 1-18. ISSN: 1417-3875.
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IRAGI, M.; HOLGATE, D.; ŠLAPAL, J. Topogenous orders on forms. Mathematica Slovaca, 2025, vol. 75, no. 1, p. 179-188. ISSN: 0139-9918.
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ŠREMR, J. Positive periodic solutions to super-linear second-order ODEs. Czechoslovak Mathematical Journal, 2025, vol. 75, no. 1, p. 257-275. ISSN: 0011-4642.
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BRDEČKOVÁ, J.; HRDINA, J. Notes on the losses compensation of a three-phase power system with DC offset based on geometric algebras*. Nonlinear Analysis - Modelling and Control, 2025, vol. 30, no. 2, p. 252-269. ISSN: 1392-5113.
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KUREŠ, M. Instructions for carpenters on how to cut a tetrahedron. MATerials MATemàtics, 2025, vol. 2025, no. 3, p. 1-5. ISSN: 1887-1097.
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ŘEHÁK, P. Fractional Integration and Differentiation of Asymptotic Relations and Applications. Mathematical Methods in the Applied Sciences, 2025, vol. 48, no. 6, p. 6381-6395. ISSN: 1099-1476.
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ŠREMR, J. On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point. APPLICATIONS OF MATHEMATICS, 2025, vol. 70, no. 1, p. 11-45. ISSN: 0862-7940.
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SCHMIDLOVÁ, S.; JAVŮRKOVÁ, Z.; TREMLOVÁ, B.; HERNIK, J.; PRUS, B.; MARCINČÁK, S.; MARCINČÁKOVÁ, D.; ŠTARHA, P.; ČÍŽKOVÁ, H.; KRUŽÍK, V.; BODOR, Z.; BENEDEK, C.; TITĚRA, D.; BORŽÍKOVÁ, J.; POSPIECH, M. Exploring the Influence of Soil Types on the Mineral Profile of Honey: Implications for Geographical Origin Prediction. Foods, 2024, vol. 13, no. 13, ISSN: 2304-8158.
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KLAŠKA, J. Aplikace celočíselných bodů eliptických křivek v teorii kubických a kvartických polynomů. Kvaternion, 2025, roč. 1, č. 1-2, s. 19-40. ISSN: 1805-1324.
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SUJA, J.; KULMON, P. Scalarization of Multi-Function Sensor Scheduling Problem. In Proceedings of the International Conference on New Trends in Signal Processing, NTSP 2024. NEW YORK: IEEE, 2024. p. 160-164. ISBN: 978-80-8040-637-0.
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KOČENDOVÁ, A.; KUREŠ, M. Inverze matic nad nekomutativními okruhy pomocí Schurových doplňků. Kvaternion, 2024, roč. 2024, č. 1-2, s. 73-82. ISSN: 1805-1324.
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HRABEC, D.; KUČERA, J.; MARTÍNEK, P. Marketing effort within the newsvendor problem framework: A systematic review and extensions of demand-effort and cost-effort formulations. INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS, 2023, vol. 257, no. 2023, p. 1-10. ISSN: 1873-7579.
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OPLUŠTIL, Z. ON NON-OSCILLATION FOR TWO DIMENSIONAL SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS. Miskolc Mathematical Notes (electronic version), 2024, vol. 25, no. 2, p. 943-954. ISSN: 1787-2413.
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JURAČKA, J.; HÜBNEROVÁ, Z. FUEL CONSUMPTION MONITORING OF TURBOPROP ENGINE. In ICAS Proceedings. ICAS proceedings. DLR, 2024. ISSN: 1025-9090.
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ŠTOUDKOVÁ RŮŽIČKOVÁ, V. SYMMETRIC 2 x 2 MATRIX FUNCTIONS WITH ORDER PRESERVING PROPERTY. Opuscula Mathematica, 2024, vol. 44, no. 6, p. 853-882. ISSN: 1232-9274.
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ČERMÁK, J.; FEDORKOVÁ, L.; JÁNSKÝ, J. On moduli and arguments of roots of complex trinomials. PACIFIC JOURNAL OF MATHEMATICS, 2024, vol. 332, no. 1, p. 39-67. ISSN: 0030-8730.
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ČERMÁK, J.; ANDRES, J.; FEDORKOVÁ, L. Piers Bohl stále inspirující. Pokroky matematiky, fyziky a astronomie, 2024, roč. 69, č. 3, s. 133-152. ISSN: 0032-2423.
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Responsibility: Vašík Petr, doc. Mgr., Ph.D.