Publications

• 2024

  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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  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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  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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  HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; ZALABOVÁ, L. A note on geometric algebras and control problems with SO(3)-symmetries. Mathematical Methods in the Applied Sciences, 2024, vol. 47, no. 3, p. 1257-1273. ISSN: 1099-1476.
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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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  DEREVIANKO, A.; VAŠÍK, P. Solver-free optimal control for linear dynamical switched system by means of geometric algebra. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, vol. 47, no. 3, p. 1274-1288. ISSN: 0170-4214.
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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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  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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• 2023

  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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  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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• 2022

  BYRTUS, R.; DEREVIANKO, A.; VAŠÍK, P.; HILDENBRAND, D.; STEINMETZ, C. On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb. ADV APPL CLIFFORD AL, 2022, vol. 32, no. 1, p. 1-21. ISSN: 0188-7009.
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  HRDINA, J.; VAŠÍK, P.; NÁVRAT, A. Quantum computing based on complex Clifford algebras. Quantum Information Processing, 2022, vol. 21, no. 9, p. 1-21. ISSN: 1573-1332.
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• 2021

  LOUČKA, P.; VAŠÍK, P. Algorithms for Multi-conditioned Conic Fitting in Geometric Algebra for Conics. In Advances in Computer Graphics. Lecture Notes in Computer Science. Switzerland: Springer, Cham, 2021. p. 645-657. ISBN: 978-3-030-89028-5.
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  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.; DORST, L. Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra. ADV APPL CLIFFORD AL, 2021, vol. 31, no. 18, p. 1-13. ISSN: 0188-7009.
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• 2020

  HRDINA, J.; VAŠÍK, P.; PROCHÁZKA, J.; KUTĚJ, L.; ŠČUREK, R. The weighted core of games based on tactical decisions. In Modelling and Simulation for Autonomous Systems. Information Systems and Applications, incl. Internet/Web, and HCI. Switzerland: Springer Nature Switzerland AG, 2020. p. 244-252. ISBN: 978-3-030-43889-0.
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  BYRTUS, R.; DEREVIANKO, A.; VAŠÍK, P. Outline of Tube Elbow Detection Based on GAC. In Advances in Computer Graphics. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Switzerland: Springer Science and Business Media Deutschland GmbH, 2020. p. 482-491. ISBN: 978-3-030-61863-6.
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• 2019

  HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; HILDENBRAND, D. Local Controllability of Snake Robots Based on CRA, Theory and Practice. ADV APPL CLIFFORD AL, 2019, vol. 30, no. 1, p. 1-21. ISSN: 0188-7009.
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  HRDINA, J.; VAŠÍK, P.; NÁVRAT, A. GAC Application to Corner Detection Based on Eccentricity. In Advances in Computer Graphics. Lecture Notes in Computer Science. Switzerland: Springer Nature Switzerland AG 2019, 2019. p. 564-570. ISBN: 978-3-030-22513-1.
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  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P. Conic Fitting in Geometric Algebra Setting. ADV APPL CLIFFORD AL, 2019, vol. 29, no. 4, p. 1-13. ISSN: 0188-7009.
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• 2018

  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P. Notes on Planar Inverse Kinematics Based on Geometric Algebra. ADV APPL CLIFFORD AL, 2018, vol. 28, no. 3, p. 71-85. ISSN: 0188-7009.
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  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P. Geometric Algebra for Conics. ADV APPL CLIFFORD AL, 2018, vol. 28, no. 3, p. 66-87. ISSN: 0188-7009.
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  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P. CRA-based robotic snake control. In Introduction to Geometric Algebra Computing. Boca Raton, USA: Chapman and Hall/CRC, 2018. p. 141-154. ISBN: 9781498748384.
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  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.; MATOUŠEK, R. Fisheye correction by CGA non-linear transformation. Mathematical Methods in the Applied Sciences, 2018, vol. 41, no. 11, p. 4106-4116. ISSN: 1099-1476.
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  HRDINA, J.; VAŠÍK, P.; MATOUŠEK, R.; NÁVRAT, A. Geometric algebras for uniform colour spaces. Mathematical Methods in the Applied Sciences, 2018, vol. 41, no. 11, p. 4117-4130. ISSN: 1099-1476.
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• 2017

  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.; MATOUŠEK, R. Local control of (4,5,7,8-10)-filtration snake robot via CGA. Mendel Journal series, 2017, vol. 23, no. 1, p. 157-162. ISSN: 1803-3814.
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  NÁVRAT, A.; VAŠÍK, P. On geometric control models of a robotic snake. Note di Matematica, 2017, vol. 37, no. Suppl. 1, p. 119-129. ISSN: 1123-2536.
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  HRDINA, J.; MATOUŠEK, R.; NÁVRAT, A.; VAŠÍK, P. Nilpotent approximation of a trident snake robot controlling distribution. Kybernetika, 2017, vol. 53, no. 6, p. 1118-1130. ISSN: 0023-5954.
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  HRDINA, J.; VAŠÍK, P.; HOLUB, M. Dual numbers arithmentic in multiaxis machine error modeling. MM Science Journal, 2017, vol. 2017, no. 1, p. 1769-1772. ISSN: 1803-1269.
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  HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.; MATOUŠEK, R. Geometric Control of the Trident Snake Robot Based on CGA. ADV APPL CLIFFORD AL, 2017, vol. 27, no. 1, p. 633-645. ISSN: 0188-7009.
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  HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; MATOUŠEK, R. CGA- based robotic snake control. ADV APPL CLIFFORD AL, 2017, vol. 27, no. 1, p. 621-632. ISSN: 0188-7009.
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• 2016

  HRDINA, J.; VAŠÍK, P.; NÁVRAT, A. Control of 3-Link Robotic Snake Based on Conformal Geometric Algebra. ADV APPL CLIFFORD AL, 2016, vol. 26, no. 3, p. 1069-1080. ISSN: 0188-7009.
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• 2015

  HRDINA, J.; VAŠÍK, P. Notes on differential kinematics in conformal geometric algebra approach. In Mendel 2015. Recent Advances in Soft Computing. Switzerland: Springer International Publishing, 2015. p. 363-374. ISBN: 978-3-319-19824-8.
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  HOLUB, M.; HRDINA, J.; VAŠÍK, P.; VETIŠKA, J. Three-axes error modeling based on second order dual numbers. Journal of Mathematics in Industry, 2015, vol. 5, no. 2, p. 1-11. ISSN: 2190-5983.
  Detail | WWW | Full text in the Digital Library

  HRDINA, J.; VAŠÍK, P.; MATOUŠEK, R. Special orthogonal matrices over dual numbers and their applications. Mendel Journal series, 2015, vol. 2015, no. 6, p. 121-126. ISSN: 1803- 3814.
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• 2014

  HRDINA, J.; VAŠÍK, P. Dual Numbers Approach in Multiaxis Machines Error Modeling. Journal of Applied Mathematics, 2014, vol. 2014, no. 1, p. 1-6. ISSN: 1110-757X.
  Detail | WWW | Full text in the Digital Library

  RAHULA, M.; VAŠÍK, P. A note on jet and geometric approach to higher order connections. In Algebra, Geometry and Mathematical Physics. Springer Proceedings in Mathematics and Statistics. Germany: Springer - Verlag, 2014. p. 375-385. ISBN: 978-3-642-55360- 8.
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  RAHULA, M.; VAŠÍK, P. Connections in control strategy. Proceedings of the Estonian Academy of Sciences, 2014, vol. 63, no. 1, p. 26-32. ISSN: 1736-6046.
  Detail | WWW | Full text in the Digital Library

  HRDINA, J.; VAŠÍK, P. Geometry of almost Cliffordian manifolds: classes of subordinated connections. TURKISH JOURNAL OF MATHEMATICS, 2014, vol. 38, no. 1, p. 179-190. ISSN: 1300- 0098.
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• 2013

  VAŠÍK, P. Higher order connections on Lie groupoid: application to materials. Miskolc Mathematical Notes, 2013, vol. 14, no. 2, p. 705-711. ISSN: 1787- 2405.
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  HRDINA, J.; VAŠÍK, P. Semiholonomic second order connections associated to materia bodies. J APPL MATH, 2013, vol. 2013, no. 1, p. 1-5. ISSN: 1110- 757X.
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• 2012

  RAHULA, M.; VAŠÍK, P.; VOICU, N. Tangent structures: sector-forms, jets and connections. Journal of Physics: Conference Series, 2012, vol. 2012, no. 346, p. 1-9. ISSN: 1742- 6588.
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  HRDINA, J.; VAŠÍK, P. Generalized geodesics on almost Cliffordian geometries. Balkan Journal of Geometry, and Its Applications, 2012, vol. 17 (2012), no. 1, p. 41-48. ISSN: 1224- 2780.
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• 2011

  VAŠÍK, P. On third order semiholonomic prolongation of a connection. Banach Center Publications, 2011, vol. 93, no. 2011, p. 271-276. ISSN: 0137- 6934.
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  POLZER, A.; VAŠÍK, P. Progresivní frézování. In Vysoce přesné technologie obrábění; Programování moderních CNC strojů. 1. Brno: Ing. Vladislav Pokorný - LITERA Brno, 2011. p. 91-92. ISBN: 978-80-214-4352- 5.
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• 2010

  VAŠÍK, P. Transformations of semiholonomic 2 and 3- jets and semiholonomic prolongation of connections. Proceedings of the Estonian Academy of Sciences, 2010, vol. 59, no. 4, p. 375-380. ISSN: 1736- 6046.
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  HRDINA, J.; KUREŠ, M.; VAŠÍK, P. A note on tame polynomial automorphisms and the security of TTM cryptosystem. APPLIED AND COMPUTATIONAL MATHEMATICS, 2010, vol. 9, no. 2, p. 226-233. ISSN: 1683- 3511.
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• 2007

  VAŠÍK, P. On the Ehresmann Prolongation. Annales Universitatis Mariae Curie Sklodowska, 2007, vol. LXI, no. Sectio A, p. 145-153. ISSN: 0365- 1029.
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  CIHLÁŘOVÁ, P.; VAŠÍK, P. Technologie výroby složitých tvarových nástrojů s využitím diferenciálního počtu. In FSI Junior konference 2006. Brno: FSI VUT v Brně, 2007. p. 16-20. ISBN: 978-80-214-3364- 9.
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• 2006

  VAŠÍK, P. Connections on Higher Order Principal Prolongations. Vědecké spisy Vysokého učení technického v Brně , Edice PhD Thesis. Edice PhD Thesis. 2006. p. 1-27. ISBN: 80-214-3196- 2. ISSN: 1213- 4198.
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  VAŠÍK, P. Connections on higher order principal prolongations. Supplemento ai Rendiconti del Circolo Matematico di Palermo, 2006, vol. 79, no. Suppl. 79, p. 183-192. ISSN: 0009- 725X.
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  VAŠÍK, P.; PÍŠKA, M.; CIHLÁŘOVÁ, P. Parametrický popis ploch pomocí systému MAPLE. In Sborník z 15. seminářee Moderní matematické metody v inženýrství. Ostrava: VŠB - Technická univerzita OStrava, 2006. p. 211-215. ISBN: 80-248-1224- X.
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• 2005

  POLZER, A.; CIHLÁŘOVÁ, P.; VAŠÍK, P. Elektronová fázová a strukturní analýza celokarbidových nástrojů. In FSI Junior konference 2004. Brno: FSI VUT v Brně, 2005. p. 1-6. ISBN: 80-214-2934- 8.
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  PÍŠKA, M., POLZER, A. Analýza plochy řezu vznikající při obrábění frézou s kulovým čelem. In Moderní matematické metody v inženýrství. Ostrava: VŠB TU Ostrava, 2005. p. 214-217. ISBN: 80-248-0951- 6.
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  CIHLÁŘOVÁ, P.; POLZER, A.; VAŠÍK, P. Komplexní analýza řezivostních vlastností moderních HSS fréz. In FSI Junior konference 2004. Brno: FSI VUT v Brně, 2005. p. 10-14. ISBN: 80-214-2934- 8.
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