Project detail

Pokročilé matematické metody pro řešení úloh v inženýrství

Duration: 01.03.2023 — 28.02.2026

Funding resources

Brno University of Technology - Vnitřní projekty VUT

- whole funder (2023-01-01 - 2024-12-31)

On the project

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.

Mark

FSI-S-23-8161

Default language

Czech

People responsible

Benko Matej, Ing. - fellow researcher
Byrtus Roman, Ing. - fellow researcher
Čermák Jan, prof. RNDr., CSc. - fellow researcher
Derevianko Anna, Ing. - 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. - fellow researcher
Kureš Miroslav, doc. RNDr., Ph.D. - fellow researcher
Loučka Pavel, Ing. - 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
Žák Libor, doc. RNDr., Ph.D. - fellow researcher
Vašík Petr, doc. Mgr., Ph.D. - principal person responsible

Units

Institute of Mathematics
- (2023-01-01 - 2025-12-31)
Faculty of Mechanical Engineering
- (2023-01-01 - 2025-12-31)

Results

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W. On Weil like functors on flag vector bundles with given length. FILOMAT, 2023, vol. 37, no. 9, p. 2755-2771. ISSN: 0354-5180.
Detail

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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IRAGI, M., ŠLAPAL, J. Transitive quasi-uniform structures depending on a parameter. AEQUATIONES MATHEMATICAE, 2023, vol. 97, no. 4, p. 823-836. ISSN: 0001-9054.
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LOUČKA, P.; VAŠÍK, P. On Multi-conditioned Conic Fitting in Geometric Algebra for Conics. ADV APPL CLIFFORD AL, 2023, vol. 33, no. 3, ISSN: 0188-7009.
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DOUPOVEC, M.; KUREK, J.; MIKULSKI, W. Natural affinors and torsion of connections on Weil like functors on double vector bundles. Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica, 2023, vol. 76, no. 2, p. 1-13. ISSN: 2083-7402.
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HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; ERYGANOV, I.; HILDENBRAND, D.; ALVES, R.; LAVOR, C.; STEINMETZ, C. Quantum Register Algebra: the mathematical language for quantum computing. Quantum Information Processing, 2023, vol. 22, no. 9, p. 1-27. ISSN: 1573-1332.
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ŘEHÁK, P. On decaying and asymptotically constant solutions of nonlinear equations with the Weyl fractional derivative of an order in (1,2). APPLIED MATHEMATICS LETTERS, 2023, vol. 145, no. 108779, p. 1-9. ISSN: 0893-9659.
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KUREŠ, M. A Proof of Pollock’s Conjecture on Centered Nonagonal Numbers. MATHEMATICAL INTELLIGENCER, 2023, no. 2023, p. 1-2. ISSN: 0343-6993.
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FROLÍK, S.; HRDINA, J. Local control of 2-link robotic worms based on additional symmetries *. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2023, vol. 360, no. 16, p. 12280-12298. ISSN: 0016-0032.
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PAVLÍK, J. Distributivity of a segmentation lattice. Discrete Applied Mathematics, 2023, vol. 339, no. 0166-218X, p. 300-316. ISSN: 0166-218X.
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ŠLAPAL, J. A digital Jordan surface theorem with respect to a graph connectedness. Open Mathematics, 2023, vol. 21, no. 1, p. 1-9. ISSN: 2391-5455.
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LOUČKA, P.; VAŠÍK, P. Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics. Advances in Applied Clifford Algebras, 2024, vol. 34, no. 1, p. 1-22. ISSN: 1661-4909.
Detail

KLAŠKA, J. The Full Systems of Canonical Representatives of Cubic Polynomials with a Given Discriminant. Brno, Česká republika: Akadenické nakladatelství CERM, 2023. 150 p. ISBN: 978-80-7623-097-2.
Detail

KLAŠKA, J. JAKÓBCZYKOVA HYPOTÉZA O FERMATOVÝCH ČÍSLECH. Kvaternion, 2023, č. 1-2, s. 3-13. ISSN: 1805-1324.
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KLAŠKA, J. Jakobczyk's Hypothesis on Mersenne Numbers and Generalizations of Skula's Theorem. Journal of Integer Sequences, 2023, vol. 26, no. 3, p. 1-21. ISSN: 1530-7638.
Detail

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W. Description of jet like functors on vector bundles by means of module bundle functors on the bases. FILOMAT, 2024, vol. 38, no. 1, p. 241-260. ISSN: 0354-5180.
Detail

PROCHÁZKOVÁ, J.; KŘIŠŠÁK, J. The Artificial Intelligence Algorithm Used for Harvested Wood Recognition. PEFnet 2023. 1... Brno, CZ3-.: Mendel University Press, 2023. p. 91-92. ISBN: 978-80-7509-944-0.
Detail

RŮŽIČKOVÁ, M.; KÚDELČÍKOVÁ, M.; ŠTOUDKOVÁ RŮŽIČKOVÁ, V. Spojité dynamické systémy. Stabilita, aplikácie. Vedecké monografie. Vedecké monografie. Žilina: EDIS-vydavateľstvo UNIZA, 2023. 248 s. ISBN: 978-80-554-2063-9.
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FROLÍK, S.; HRDINA, J. SUB-RIEMANNIAN GEODESICS ASSOCIATED TO CR-GEOMETRY ON HEISENBERG GROUP H3. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2024, vol. 85, no. 4, p. 55-66. ISSN: 1223-7027.
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KULMON, P.; SUJA, J.; BENKO, M. Scheduling of Multi-Function Sensor. IEEE Transactions on Radar Systems, 2023, vol. 1, no. 1, p. 729-739. ISSN: 2832-7357.
Detail

MAZAL, J.; FAGIOLINI, A.; VAŠÍK, P.; BRUZZONE, A.; PICKL, S.; NEUMANN, V.; STODOLA, P.; STORTO, S. Preface. Deutschland: Springer Science and Business Media Deutschland GmbH, 2023. p. 1 (1 s.).
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HITZER, E.; PAPAGIANNAKIS, G.; VAŠÍK, P. Preface. Switzerland: Springer Cham, 2023. p. 1 (1 s.).
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LOUČKA, P. On Proper and Improper Points in Geometric Algebra for Conics and Conic Fitting Through Given Waypoints. In EmpoweringNovel GeometricAlgebrafor GraphicsandEngineering. Lecture Notes in Computer Science. Switzerland: Springer, Cham, 2023. p. 67-79. ISBN: 978-3-031-30922-9.
Detail

MACHÁLEK, L.; KONECKÝ, Š. Autonomous Navigation for the Movement of the Robot in the Tube. In Modelling and Simulation for Autonomous Systems. Springer Cham, 2023. p. 74-86. ISBN: 978-3-031-31267-0.
Detail

VAŠÍK, P.; HITZER, E.; LAVOR, C. Editorial of Applied Geometric Algebras in Computer Science and Engineering (AGACSE 21). Mathematical Methods in the Applied Sciences. HOBOKEN: WILEY, 2024. p. 1199-1203. ISSN: 1099-1476.
Detail

DEREVIANKO, A.; VAŠÍK, P. Search for Similarity Transformation Between Image Point Clouds Using Geometric Algebra for Conics. In Advanced Computational Applications of Geometric Algebra. Lecture Notes in Computer Science. CHAM: SPRINGER INTERNATIONAL PUBLISHING AG, 2024. p. 15-26. ISBN: 978-3-031-34031-4.
Detail

BYRTUS, R.; FROLÍK, S. Notes on Forward Kinematics of Generalised Robotic Snakes Based on Compass Ruler Algebra. In Advanced Computational Applications of Geometric Algebra. Lecture Notes in Computer Science. CHAM: SPRINGER INTERNATIONAL PUBLISHING AG, 2024. p. 138-146. ISBN: 978-3-031-34031-4. ISSN: 1611-3349.
Detail

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.
Detail

ŠTARHA, P.: ASI_CorCap_2023; ASI Corona Capture version 2023. Ústav matematiky Fakulta strojního inženýrství Technická 2896/2 61669 Brno. URL: http://www.zam.fme.vutbr.cz/~starha/asi_corcap/. (software)
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