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.

Popis anglicky
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

čeština

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

Ústav matematiky
- odpovědné pracoviště (1.2.2024 - nezadáno)
Ústav matematiky
- interní (1.1.2023 - 31.12.2025)
Fakulta strojního inženýrství
- příjemce (1.1.2023 - 31.12.2025)

BENKO, M.; HÜBNEROVÁ, Z.; WITKOVSKÝ, V. Characteristic function and moment generating function of multivariate folded normal distribution. STATISTICAL PAPERS, 2025, vol. 66, no. 4, p. 1-23. ISSN: 0932-5026.
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BENKO, M.; CHLEBICKA, I.; MIASOJEDOW, B.; ENDAL, J. Langevin Monte Carlo Beyond Lipschitz Gradient Continuity. In Proceedings of the 39th Annual AAAI Conference on Artificial Intelligence. Philadelphia: Association for the Advancement of Artificial Intelligence, 2025. p. 15541-15549. ISBN: 978-1-57735-897-8.
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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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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, p. 781-803. 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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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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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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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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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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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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HITZER, E.; PAPAGIANNAKIS, G.; VAŠÍK, P. Preface. Switzerland: Springer Cham, 2023. p. 1 (1 s.).
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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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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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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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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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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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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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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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KLAŠKA, J. JAKÓBCZYKOVA HYPOTÉZA O FERMATOVÝCH ČÍSLECH. Kvaternion, 2023, č. 1-2, s. 3-13. ISSN: 1805-1324.
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Odpovědnost: Vašík Petr, doc. Mgr., Ph.D.