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Project detail
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.
Description in EnglishThe 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
Benko Matej, Ing. - fellow researcherByrtus Roman, Ing. - fellow researcherČermák Jan, prof. RNDr., CSc. - fellow researcherDerevianko Anna, Ing. - fellow researcherDruckmüller Miloslav, prof. RNDr., CSc. - fellow researcherEryganov Ivan, Ing., Ph.D. - fellow researcherFedorková Lucie, Ing. - fellow researcherFranců Jan, prof. RNDr., CSc. - fellow researcherHrdina Jaroslav, doc. Mgr., Ph.D. - fellow researcherKalenská Petra, Ing. - fellow researcherKureš Miroslav, doc. RNDr., Ph.D. - fellow researcherLoučka Pavel, Ing. - fellow researcherMachovičová Tatiana, Ing. - fellow researcherMaya Baraah - fellow researcherNavrátil Dušan, Ing. - fellow researcherPetrák Filip, Mgr. - fellow researcherŠlapal Josef, prof. RNDr., CSc. - fellow researcherŠtarha Pavel, doc. Ing., Ph.D. - fellow researcherTomáš Jiří, doc. RNDr., Dr. - fellow researcherŽák Libor, doc. RNDr., Ph.D. - fellow researcherVašík 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
ŘEHÁK, P. The discrete fractional Karamata theorem and its applications. Mathematica Slovaca, 2024, vol. 74, no. 5, p. 1205-1214. ISSN: 0139-9918.Detail
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.Detail
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.Detail
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.Detail
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.Detail
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.Detail
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.Detail
KUREŠ, M. A Proof of Pollock’s Conjecture on Centered Nonagonal Numbers. MATHEMATICAL INTELLIGENCER, 2023, no. 2023, p. 1-2. ISSN: 0343-6993.Detail
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.Detail
PAVLÍK, J. Distributivity of a segmentation lattice. Discrete Applied Mathematics, 2023, vol. 339, no. 0166-218X, p. 300-316. ISSN: 0166-218X.Detail
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.Detail
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.Detail
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.Detail
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.Detail
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.).Detail
HITZER, E.; PAPAGIANNAKIS, G.; VAŠÍK, P. Preface. Switzerland: Springer Cham, 2023. p. 1 (1 s.).Detail
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
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.Detail
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.Detail
RICHMOND, T.; ŠLAPAL, J. Lower separation axioms in bitopogenous spaces. Mathematica Slovaca, 2024, vol. 74, no. 2, p. 491-500. ISSN: 1337-2211.Detail
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.Detail
OPLUŠTIL, Z. Oscillation criteria for the second-order linear advanced differential equation. APPLIED MATHEMATICS LETTERS, 2024, vol. 157, no. 157, ISSN: 0893-9659.Detail
ŠLAPAL, J. DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING. Mathematica Slovaca, 2024, vol. 74, no. 3, p. 723-736. ISSN: 1337-2211.Detail
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.Detail
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.Detail
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.Detail
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.Detail
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.Detail
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.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)Detail