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. - 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)

JURAČKA, J.; HÜBNEROVÁ, Z. FUEL CONSUMPTION MONITORING OF TURBOPROP ENGINE. 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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KOVÁŘ, J.; FUIS, V. Influence of Berkovich indenter tilt on the projected contact area at nanoindentation test. Engineering mechanics 2024. Milovy: Brno University of Technology, 2024. p. 166-169. ISBN: 978-80-214-6235-9.
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MOURALOVÁ, K.; BENEŠ, L.; BEDNÁŘ, J; ZAHRADNÍČEK, R.; FRIES, J. Influence of different wire materials on the machining of Albromet W130 by WEDM. PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE, 2024, vol. 238, no. 14, ISSN: 0954-4054.
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KALENSKÁ, P.; RAJMIC, P.; GEBRTOVÁ, K.; DRUCKMÜLLER, M. A Novel Technique for the Extraction of Dynamic Events in Extreme Ultraviolet Solar Images. Astrophysical Journal, Supplement Series, 2024, vol. 275, no. 1, ISSN: 1538-4365.
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ŘEHÁK, P. The discrete fractional Karamata theorem and its applications. Mathematica Slovaca, 2024, vol. 74, no. 5, p. 1205-1214. ISSN: 0139-9918.
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ŠLAPAL, J. A digital 3D Jordan-Brouwer separation theorem. Analele Stiintifice Ale Universitatii Ovidius Constanta, Seria Matematica, 2024, vol. 32, no. 3, p. 161-172. ISSN: 1224-1784.
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ERYGANOV, I.; HRDINA, J.; NÁVRAT, A. Quantization of two- and three-player cooperative games based on QRA. Journal of Physics A: Mathematical and Theoretical, 2024, vol. 57, no. 42, p. 1-24. ISSN: 1751-8121.
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MOURALOVÁ, K.; BEDNÁŘ, J; BENEŠ, L.; ZAHRADNÍČEK, R.; FRIES, J. Machinability analysis of Albromet W130 copper alloy by WEDM. INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY, 2024, vol. 134, no. 11, p. 5771-5785. ISSN: 0268-3768.
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HRDINA, J.; STODOLA, M. Higher Order Geometric Algebras and Their Implementations Using Bott Periodicity. ADV APPL CLIFFORD AL, 2024, vol. 34, no. 4, p. 1-22. ISSN: 0188-7009.
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HITZER, E.; PAPAGIANNAKIS, G.; VAŠÍK, P. Editorial for special issue "ENGAGE 22: Geometric Algebra for Graphics & Engineering". Mathematical Methods in the Applied Sciences. HOBOKEN: WILEY, 2024. p. 11303-11304. ISSN: 1099-1476.
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ERYGANOV, I.; ROSECKÝ, M.; ŠOMPLÁK, R.; SMEJKALOVÁ, V. Forecasting the waste production hierarchical time series with correlation structure. OPTIMIZATION AND ENGINEERING, 2024, no. July 2024, ISSN: 1573-2924.
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ŠLAPAL, J. DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING. Mathematica Slovaca, 2024, vol. 74, no. 3, p. 723-736. ISSN: 1337-2211.
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OPLUŠTIL, Z. Oscillation criteria for the second-order linear advanced differential equation. APPLIED MATHEMATICS LETTERS, 2024, vol. 157, no. 157, ISSN: 0893-9659.
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VENTURA GIL, J.; MARTINEZ, F.; MANZANO-AGUGLIARO, F.; NÁVRAT, A.; HRDINA, J.; EID, A.; MONTOYA, F. A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions. JOURNAL OF GEODESY, 2024, vol. 98, no. 6, p. 1-21. ISSN: 0949-7714.
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RICHMOND, T.; ŠLAPAL, J. Lower separation axioms in bitopogenous spaces. Mathematica Slovaca, 2024, vol. 74, no. 2, p. 491-500. ISSN: 1337-2211.
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ŠLAPAL, J.; RICHMOND, T.; IRAGI, M. Topogenous orders and closure operators on posets. Turkish Journal of Mathematics, 2024, vol. 48, no. 3, p. 469-476. ISSN: 1303-6149.
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MIKULÁČEK, P.; ZEMEK, M.; ŠTARHA, P.; ZIKMUND, T.; KAISER, J. Application of Dual-target Computed Tomography for Material Decomposition of Low-Z Materials. JOURNAL OF NONDESTRUCTIVE EVALUATION, 2024, vol. 43, no. 2, ISSN: 0195-9298.
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HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; ERYGANOV, I.; ALVES, R.; HILDENBRAND, D.; STEINMETZ, C.; LAVOR, C. Quantum Register Algebra: The Basic Concepts. In Advanced Computational Applications of Geometric Algebra. CHAM: SPRINGER INTERNATIONAL PUBLISHING AG, 2024. p. 112-122. ISBN: 978-3-031-34030-7.
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TOMÁŠ, J.; PETRÁK, F. Higher-order and Weil Grassmannian as a space of subalgebras of a Weil algebra. FILOMAT, 2024, vol. 38, no. 22, p. 7755-7773. ISSN: 0354-5180.
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Responsibility: Vašík Petr, doc. Mgr., Ph.D.