Project - Pokročilé matematické metody pro řešení úloh v inženýrství

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.

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.

Mark

FSI-S-23-8161

Default language

Czech

People responsible

Units

Institute of Mathematics
- internal (2023-01-01 - 2025-12-31)
Faculty of Mechanical Engineering
- beneficiary (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.
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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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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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HITZER, E.; KAMARIANAKIS, M.; PAPAGIANNAKIS, G.; VAŠÍK, P. Survey of new applications of geometric algebra. Mathematical Methods in the Applied Sciences, 2024, vol. 47, no. 14, p. 1-17. ISSN: 1099-1476.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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.
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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Responsibility: Vašík Petr, doc. Mgr., Ph.D.

FCH VUT

Advanced Mathematical Methods for Solving Engineering Problems