Podstatou navrhovaného projektu je výzkum v oblasti moderních partií aplikované matematiky s cílem nalezení nových metod pro modelování a řešení problémů technických a přírodních věd. Pracovat budeme jejména v oblastech zpracování digitálních obrazů, řešení diferenciálních rovnic, statistiky, optimalizace a aplikací lineární algebry a diferenciální geometrie v robotice. Jedná se o pokračování výzkumu, který na Ústavu matematiky probíhá již řadu let a do kterého budou zapojeni studenti doktorského studijního programu Aplikovaná matematika.

FSI-S-17-4464

čeština

Šlapal Josef, prof. RNDr., CSc. - hlavní řešitel
Bednář Josef, Ing., Ph.D. - spoluřešitel
Čermák Jan, prof. RNDr., CSc. - spoluřešitel
Druckmüller Miloslav, prof. RNDr., CSc. - spoluřešitel
Holec Tomáš, Ing. - spoluřešitel
Hošek Jaromír, Ing. - spoluřešitel
Hrabec Pavel, Ing., Ph.D. - spoluřešitel
Hrdina Jaroslav, doc. Mgr., Ph.D. - spoluřešitel
Kokrda Lukáš, Ing. - spoluřešitel
Kratochvíl Jiří Jaroslav, Mgr., Ph.D. - spoluřešitel
Kůdela Jakub, doc. Ing., Ph.D. - spoluřešitel
Kureš Miroslav, doc. RNDr., Ph.D. - spoluřešitel
Navrátilová Barbora, Ing. - spoluřešitel
Nechvátal Luděk, doc. Ing., Ph.D. - spoluřešitel
Popela Pavel, RNDr., Ph.D. - spoluřešitel
Šútora Jan, Ing. - spoluřešitel

Ústav matematiky
- odpovědné pracoviště (2.10.2017 - nezadáno)
Ústav matematiky
- interní (1.1.2017 - 31.12.2019)
Fakulta strojního inženýrství
- příjemce (1.1.2017 - 31.12.2019)

ŠLAPAL, J.: 18th International Workshop on Combinatorial Image Analysis. Plovdiv (19.06.2017)
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ŠLAPAL, J.: 2018 International Conference on Applied Mathematics & Computational Science (ICAMCS.NET 2018). Budapest (06.10.2018)
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ŠLAPAL, J., Barneva,R., Brimkov, V., Kulczycki, P., Tavares, J.M.R.S.: 6th International Symposium on Computational Modeling of Objects Represented in Images. Fundamentals, Methods and Applications (CompIMAGE 2018). Cracow (02.06.2018)
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MOURALOVÁ, K.; BENEŠ, L.; ZAHRADNÍČEK, R.; BEDNÁŘ, J.; ZÁDĚRA, A.; FRIES, J.; KAŇA, V. WEDM used for machining high entropy alloys. Materials, 2020, vol. 13, no. 21, p. 1-20. ISSN: 1996-1944.
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KUREŠ, M.; ŠÚTORA, J. On some connected groups of automorphisms of Weil algebras. Transylvanian Journal of Mathematics and Mechanics, 2019, vol. 11, no. 1-2, p. 117-121. ISSN: 2067-239X.
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MOURALOVÁ, K.; HRABEC, P.; BENEŠ, L.; OTOUPALÍK, J.; BEDNÁŘ, J.; PROKEŠ, T.; MATOUŠEK, R. Verification of Fuzzy Inference System for Cutting Speed while WEDM for the Abrasion-Resistant Steel Creusabro by Conventional Statistical Methods. Metals, 2020, vol. 10, no. 1, p. 1-11. ISSN: 2075-4701.
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DOUPOVEC, M.; KOLÁŘ, I. ON THE γ-EQUIVALENCE OF SEMIHOLONOMIC JETS. ARCHIVUM MATHEMATICUM, 2019, vol. 55, no. 4, p. 261-264. ISSN: 0044-8753.
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OPLUŠTIL, Z. Oscillatory properties of certain system of non-linear ordinary differential equations. Miskolc Mathematical Notes, 2018, vol. 19, no. 1, p. 439-459. ISSN: 1787-2413.
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MOURALOVÁ, K.; MICHNA, S; ZAHRADNÍČEK, R.; BEDNÁŘ, J.; PLICHTA, T.; FRIES, J. Experimental analysis of microhardness changes of subsurface areas affected by WEDM. PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART E-JOURNAL OF PROCESS MECHANICAL ENGINEERING, 2022, vol. 2022, no. 236, p. 1-13. ISSN: 0954-4089.
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DOUPOVEC, M.; KUREK, J.; MIKULSKI, W. The Natural Lie Algebra Brackets on Couples of Vector Fields and p-Forms. Filomat, 2019, vol. 33, no. 9, p. 2705-2709. ISSN: 0354-5180.
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VALIŠ, D.; ŽÁK, L.; POKORA, O. Perspective approach in using anti-oxidation and anti-wear particles from oil to estimate residual technical life of a system. Tribology International, 2018, vol. 118, no. 1, p. 46-59. ISSN: 0301-679X.
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ŘEHÁK, P. The Karamata integration theorem on time scales and its applications in dynamic and difference equations. APPLIED MATHEMATICS AND COMPUTATION, 2018, vol. 338, no. -, p. 487-506. ISSN: 0096-3003.
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MOURALOVÁ, K.; BENEŠ, L.; PROKEŠ, T.; BEDNÁŘ, J.; ZAHRADNÍČEK, R.; JANKOVÝCH, R.; FRIES, J.; VONTOR, J. Analysis of the machinability of copper alloy Ampcoloy by WEDM. Materials, 2020, vol. 13, no. 4, p. 1-14. ISSN: 1996-1944.
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DOLNÍK, M.; LOMTATIDZE, A. On periodic boundary value problem for certain planar system of nonlinear ordinary differential equations. International Workshopon the Qualitative Theory of Differential Equations. 2019. p. 47-50. ISSN: 1512-3391.
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STODOLA, M. Monocular Kinematics Based on Geometric Algebra. In Modelling and Simulation for Autonomous Systems. MESAS 2018. Lecture Notes in Computer Science, vol 11472. Cham: Springer, 2019. p. 121-129. ISBN: 978-3-030-14983-3.
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KŮDELA, J.; POPELA, P.; ŠOMPLÁK, R.; MÁLEK, M.; RYCHTÁŘ, A.; HRABEC, D. The L-shaped Method for Large-scale Mixed-integer Waste Management Decision Making Problems. Chemical Engineering Transactions, 2017, vol. 61, no. 1, p. 1087-1092. ISSN: 2283-9216.
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ČERMÁK, J.; NECHVÁTAL, L. Local Bifurcations and Chaos in the Fractional Rössler System. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2018, vol. 28, no. 8, p. 1850098-1 (1850098-17 p.)ISSN: 0218-1274.
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ŘEHÁK, P.; YAMAOKA, N. Oscillation constants for second-order nonlinear dynamic equations of Euler type on time scales. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2017, vol. 23, no. 11, p. 1884-1900. ISSN: 1563-5120.
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ŘEHÁK, P. An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, vol. 454, no. 2, p. 829-882. ISSN: 0022-247X.
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KUREŠ, M. Straddled numbers: numbers equal to the sum of powers of consecutive primes from the least prime factor to the largest prime factor. Notes on Number Theory and Discrete Mathematics, 2019, vol. 25, no. 2, p. 8-15. ISSN: 1310-5132.
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BYRTUS, R.; VECHETOVÁ, J. Trident Snake Robot Motion Simulation in V-Rep. In Modelling and Simulation for Autonomous Systems. Information Systems and Applications, incl. Internet/Web, and HCI. Switzerland: Springer International Publishing, 2019. p. 27-42. ISBN: 978-3-030-14984-0.
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ŠREMR, J. Some remarks on functional differential equations in abstract spaces. Memoirs on Differential Equations and Mathematical Physics, 2017, vol. 2017, no. 72, p. 103-118. ISSN: 1512-0015.
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MOURALOVÁ, K.; PROKEŠ, T.; BENEŠ, L.; BEDNÁŘ, J. The Influence of WEDM Parameters Setup on the Occurrence of Defects when Machining Hardox 400 Steel. Materials, 2019, vol. 12, no. 22, p. 1-15. ISSN: 1996-1944.
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LOMTATIDZE, A. On periodic boundary value problem for second-order ordinary differential equations. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2020, vol. 22, no. 6, p. 1-33. ISSN: 0219-1997.
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KUREŠ, M.; DECOME, T.; DRECOURT, G. LoRi-TTM cryptosystem. Annals of the University of Craiova-Mathematics and Computer Science Series, 2018, vol. 45, no. 1, p. 137-150. ISSN: 1223-6934.
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MOURALOVÁ, K.; BENEŠ, L.; BEDNÁŘ, J.; ZAHRADNÍČEK, R.; PROKEŠ, T.; FIALA, Z.; FRIES, J. Precision Machining of Nimonic C 263 Super AlloyUsing WEDM. Coatings, MDPI, 2020, vol. 10, no. 6, p. 1-20. ISSN: 2079-6412.
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ZAHRADNÍČEK, R.; MOURALOVÁ, K.; PROKEŠ, T.; HRABEC, P.; BEDNÁŘ, J. Modelling of Magnetron TiN Deposition Using the Design of Experiment. In Recent Advances in Soft Computing and Cybernetics. Studies in Fuzziness and Soft Computing. Švýcarsko: Springer, 2021. no. 1, p. 63-70. ISBN: 978-3-030-61659-5. ISSN: 1434-9922.
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ŠLAPAL, J. CONVENIENT PRETOPOLOGIES ON Z^2. TWMS Journal of Pure and Applied Mathematics, 2018, vol. 9, no. 1, p. 40-51. ISSN: 2076-2585.
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MOURALOVÁ, K.; POLZER, A.; BENEŠ, L.; BEDNÁŘ, J.; ZAHRADNÍČEK, R.; KALIVODA, M.; FRIES, J. Multicut technology used in WEDM machining of Mar-M247. PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE, 2021, vol. 235, no. 13, p. 1-17. ISSN: 0954-4054.
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KUREŠ, M. On elliptic curves with a closed component passing through a hexagon. Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 2019, vol. 27, no. 2, p. 67-82. ISSN: 1224-1784.
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KLAŠKA, J.; SKULA, L. On the factorization of cubic polynomials with the same discriminant modulo a prime. Mathematica Slovaca, 2018, vol. 68, no. 5, p. 987-1000. ISSN: 0139-9918.
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ŘEHÁK, P. A note on transformations of independent variable in second order dynamic equations. In Springer Proceedings in Mathematics & Statistics. Cham: Springer, 2020. p. 335-353. ISBN: 978-3-030-35502-9.
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TICHÝ, R.; HILDENBRAND, D.; STEINMETZ, C. GAALOPWeb for Matlab: An Easy to Handle Solution for Industrial Geometric Algebra Implementations. Advances in Applied Clifford Algebras, 2020, vol. 30, no. 4, p. 1-18. ISSN: 0188-7009.
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KŮDELA, J.; ŠOMPLÁK, R.; NEVRLÝ, V.; LIPOVSKÝ, T. Robust Waste Transfer Station Planning by Stochastic Programming. Chemical Engineering Transactions, 2018, vol. 70, no. 1, p. 889-894. ISSN: 2283-9216.
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KLAŠKA, J. SKULA, L. LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS -- THE REAL CASE. UTILITAS MATHEMATICA, 2017, vol. 102, no. 1, p. 39-50. ISSN: 0315-3681.
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NATHALIA, A.; HABBAL, S.; DRUCKMÜLLER, M.; EMMANOUILIDIS, C.; MORGAN, H. Dynamics of Large-scale Coronal Structures as Imaged during the 2012 and 2013 Total Solar Eclipses. ASTROPHYSICAL JOURNAL, 2017, vol. 848, no. 84, p. 84-93. ISSN: 1538-4357.
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NOVÁK, J. Remark on Volumetric Errors in Kinematic Chain of MCV 754 Quick. In Modelling and Simulation for Autonomous Systems. Lecture Notes in Computer Science. Switzerland: Springer Nature Switzerland AG, 2020. p. 88-96. ISBN: 978-3-030-43889-0.
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MOURALOVÁ, K.; BENEŠ, L.; PROKEŠ, T.; BEDNÁŘ, J.; ZAHRADNÍČEK, R.; FRIES, J. Machining of pure molybdenum using WEDM. MEASUREMENT, 2020, vol. 2020, no. 163, p. 1-13. ISSN: 0263-2241.
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POPELA, P.; ŠMÍD, M. SPECIAL ISSUE: APPLIED MATHEMATICAL PROGRAMMING AND MODELLING 2016. KYBERNETIKA, 2017, vol. 53, no. 6, p. 983-984. ISSN: 0023-5954.
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PROKEŠ, T.; MOURALOVÁ, K.; ZAHRADNÍČEK, R.; BEDNÁŘ, J.; KALIVODA, M. Optimization of Deposition Parameters of a DLC Layer Using (RF) PECVD Technology. In Recent Advances in Soft Computing and Cybernetics. Studies in Fuzziness and Soft Computing. Švýcarsko: Springer International Publishing, 2021. no. 403, p. 53-62. ISBN: 978-3-030-61659-5. ISSN: 1434-9922.
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HRDINA, J.; MATOUŠEK, R.; TICHÝ, R. Colour Image Segmentation by Region Growing Based on Conformal Geometric Algebra. In Advances in Computer Graphics. LNCS. Springer Nature Switzerland AG 2019: Springer, Cham, 2019. p. 564-570. ISBN: 978-3-030-22513-1.
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KUREŠ, M. Two definitions of connections on manifolds and operations on the differential forms in local coordinates. Asia Pacific Journal of Mathematics, 2019, vol. 6, no. 11, p. 1-10. ISSN: 2357-2205.
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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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KLAŠKA, J. Donald Dines Wall's conjecture. FIBONACCI QUARTERLY, 2018, vol. 56, no. 1, p. 43-51. ISSN: 0015-0517.
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MOURALOVÁ, K.; BEDNÁŘ, J.; BENEŠ, L.; HRABEC, P.; KALIVODA, M.; FRIES, J. The analysis of EDM electrodes wear in corners and edges. Archives of Civil and Mechanical Engineering, 2020, vol. 20, no. 5, p. 1-17. ISSN: 1644-9665.
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BARTOŇOVÁ, L. Qualitative Analysis of a Robot Control Based on Sub-Riemannian Distance. In Modelling and Simulation for Autonomous Systems. Lecture Notes in Computer Science. Lecture Notes in Computer Science. Switzerland: Springer International Publishing AG, 2018. p. 193-203. ISBN: 978-3-319-76072-8. ISSN: 0302-9743.
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ŠLAPAL, J. Structuring digital plane by the 8-adjacency graph with a set of walks. International Journal of Mathematical and Computational Methods, 2017, vol. 2017, no. 2, p. 150-154. ISSN: 2367-895X.
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DOUPOVEC, M.; KUREK, J.; MIKULSKI, W. On the Courant bracket on couples of vector fields and p-forms. Annales Universitatis Mariae Curie Sklodowska, 2018, vol. 72, no. 2, p. 29-36. ISSN: 0365-1029.
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HRABEC, D.; HAUGEN, K.; POPELA, P. The newsvendor problem with advertising: an overview with extensions. Review of Managerial Science, 2017, vol. 11, no. 4, p. 767-787. ISSN: 1863-6683.
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PAVLÍK, J. Unified approach to graphs and metric spaces. Mathematica Slovaca, 2017, vol. 57, no. 5, p. 1213-1238. ISSN: 0139-9918.
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ŠLAPAL, J. Digital Jordan curves with respect to a closure operator. In NTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. Melville, NY, USA: AIP Publishing, 2020. p. 1-4. ISBN: 978-0-7354-4025-8.
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DRUCKMÜLLER, M.; HABBAL, S.; NATHALIA, A.; EMMANOUILIDIS, C. Tethered Prominence-CME Systems Captured during the 2012 November 13 and 2013 November 3 Total Solar Eclipses. Astrophysical Journal Letters, 2017, vol. 851, no. 2, p. 41-50. ISSN: 2041-8205.
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KUREŠ, M. A characterization of sliding vectors by dual numbers, some dual curves and the screw calculus. Procedia Structural Integrity, 2019, vol. 23, no. 4, p. 396-401. ISSN: 2452-3216.
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KŮDELA, J.; POPELA, P. Warm-start Cuts for Generalized Benders Decomposition. KYBERNETIKA, 2017, vol. 53, no. 6, p. 1012-1025. ISSN: 0023-5954.
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KLAŠKA, J.; SKULA, L. LAW OF INERTIA FOR THE FACTORIZATION OF CUBIC POLYNOMIALS - THE IMAGINARY CASE. UTILITAS MATHEMATICA, 2017, vol. 103, no. 2, p. 99-109. ISSN: 0315-3681.
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KLAŠKA, J. Real-world applications of number theory. South Bohemia Mathematical Letters, 2018, vol. 25, no. 1, p. 39-47. ISSN: 1804-1450.
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ŘEHÁK, P. On asymptotic relationships between two higher order dynamic equations on time scales. Applied Mathematics Letters, 2017, vol. 2017, no. 73, p. 84-90. ISSN: 0893-9659.
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Josef Šlapal. Structuring Digital Plane by Closure Operators Associated with n-ary Relations. In Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications. Lecture Notes in Computer Science. Lecture Notes in Computer Science. Svýcarsko: Springer, 2019. no. 1, p. 16-22. ISBN: 978-3-030-20804-2. ISSN: 0302-9743.
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MOURALOVÁ, K.; ZAHRADNÍČEK, R.; BEDNÁŘ, J. Study of vertical graphene growth on silver substrate based on design of experiment. DIAMOND AND RELATED MATERIALS, 2019, vol. 97, no. 3, p. 1-10. ISSN: 0925-9635.
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ŠLAPAL, J. A relational generalization of the Khalimsky topology. In Combinatorial Image Analysis. Lecture Notes in Computer Science. Lecture Notes in Computer Sciences. Switzerland: Springer, 2017. p. 132-141. ISBN: 978-3-319-59107-0. ISSN: 0302-9743.
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DOUPOVEC, M.; KUREK, J.; MIKULSKI, W. On the Symmetrization of Jets on Vector Bundles. Filomat, 2019, vol. 33, no. 4, p. 1091-1096. ISSN: 0354-5180.
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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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FROLÍK, S. Note on Signature of Trident Mechanisms with Distribution Growth Vector (4,7). In Modelling and Simulation for Autonomous Systems. MESAS 2018. Lecture Notes in Computer Science, vol 11472. Switzerland: Springer Verlag, 2019. p. 82-89. ISBN: 978-3-030-14983-3.
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VALIŠ, D.; ŽÁK, L. Contribution to prediction of soft and hard failure occurrence in combustion engine using oil tribo data. Engineering Failure Analysis, 2017, vol. 82, no. 1, p. 583-598. ISSN: 1350-6307.
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MOURALOVÁ, K.; BENEŠ, L.; BEDNÁŘ, J.; ZAHRADNÍČEK, R.; PROKEŠ, T.; FRIES, J. Analysis of Machinability and Crack Occurrence of Steels 1.2363 and 1.2343ESR Machined by Die-Sinking EDM. Coatings, MDPI, 2020, vol. 10, no. 4, p. 1-18. ISSN: 2079-6412.
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KUREŠ, M. Number theoretical views on resonant Rossby wave triads: graphs with vertices on quartics. Nonlinear Phenomena in Complex Systems, 2019, vol. 22, no. 3, p. 285-291. ISSN: 1561-4085.
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HRDINA, J.; ZALABOVÁ, L. Local Geometric Control of a Certain Mechanism with the Growth Vector (4,7). JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2020, vol. 26, no. 2, p. 199-216. ISSN: 1079-2724.
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ŠLAPAL, J. Closure operators associated to ternary relations for structuring the digital plane. In 2018 International Conference on Applied Mathematics & Computational Science, ICAMCS.NET 2018. Los Alamitos, CA, USA: Institute of Electrical and Electronics Engineers ( IEEE ), 2018. p. 125-128. ISBN: 9781538694695.
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Odpovědnost: Šlapal Josef, prof. RNDr., CSc.