doc. RNDr. Miroslav Kureš, Ph.D.
E-mail:   kures@fme.vutbr.cz  WWW:   http://www.zam.fme.vutbr.cz/~kures/ Dept.:   Institute of Mathematics Dept. of Algebra and Discrete Mathematics Position:   Associate Professor Room:   A1/1840

Supervised courses:

• Calculus of Variations (S1M)
• Calculus of Variations (S1M-A)
• Geometrical Algorithms and Cryptography (SAV)
• Geometrical Algorithms and Cryptography (SAV-A)
• Groups and Rings (SG0)
• Groups and Rings (SG0-A)
• Invariants and Symmetry (9ISY)
• Mathematical Principles of Cryptographic Algorithms (9MPK)
• Mathematics I (BC_MAT1)

Publications:

• Kureš Miroslav:
  On coordinate expressions of jet groups and their representations
• KUREŠ, M.:
  A Proof of Pollock’s Conjecture on Centered Nonagonal Numbers, Springer Nature
  journal article in Web of Science
• MAYA, B.; KUREŠ, M.:
  Some tridiagonal matrices and determinants of Schur-Cohn criterion for trinomials, University Politehnica of Bucharest
  journal article in Web of Science
• ČERMÁK, J.; FEDORKOVÁ, L.; KUREŠ, M.:
  Complete classification scheme for the distribution of trinomial zeros with respect to their moduli, KOSSUTH LAJOS TUDOMANYEGYETEM
  journal article in Web of Science
• KUREŠ, M.:
  A Note on the Remarkable Expression of the Number 8/pi(2) That the Ramanujan Machine Discovered, Springer
  journal article in Web of Science
• KUREŠ, M.:
  Cube-root-subgroups of SL_2 over imaginary quadratic integers, Vladimir Andrunakievich Institute of Mathematics and Computer Science
  journal article in Web of Science
• Kureš Miroslav:
  A note on the remarkable expression of the number 8 / π^2 that the Ramanujan Machine discovered
• KUREŠ, M.:
  On coordinate expressions of jet groups and their representations, Avanagard Prima
  journal article in Scopus
• KUREŠ, M.:
  On Münchhausen numbers, Bulgarian Academy of Sciences
  journal article in Web of Science
• KUREŠ, M.:
  A characterization of sliding vectors by dual numbers, some dual curves and the screw calculus, Elsevier
  journal article in Scopus
• KUREŠ, M.:
  Number theoretical views on resonant Rossby wave triads: graphs with vertices on quartics, "Education and Upbringing" Publishing
  journal article in Web of Science
• KUREŠ, M.:
  Straddled numbers: numbers equal to the sum of powers of consecutive primes from the least prime factor to the largest prime factor, Bulgarian Academy of Sciences
  journal article in Web of Science
• KUREŠ, M.:
  On elliptic curves with a closed component passing through a hexagon, Ovidius University
  journal article in Web of Science
• KUREŠ, M.:
  Two definitions of connections on manifolds and operations on the differential forms in local coordinates,
  Asia Pacific Journal of Mathematics, Vol.6, (2019), No.11, pp.1-10, ISSN 2357-2205, Asia Pacific Academic
  journal article - other
• KUREŠ, M.; DECOME, T.; DRECOURT, G.:
  LoRi-TTM cryptosystem, University of Craiova
  journal article in Web of Science
• KUREŠ, M.:
  Higher order frames and material symmetries, Trans Tech Publications Inc.
  journal article in Scopus
• HORNÍČEK, J.; KUREŠ, M.; MACÁLKOVÁ, L.:
  Some properties of orders of quaternion algebras with regard to the discrete norm, Institute of Mathematics, Czech Academy of Sciences
  journal article in Web of Science
• IVIČIČ, V.; KUREŠ, M.:
  Two general examples of Weil algebras having the group of automorphisms connected, World Scientific
  journal article in Web of Science
• KUREŠ, M.:
  Some Remarks to Higher Order Frames Occurring in Continuum Mechanics,
  Continuous Media with Microstructure 2, pp.45-52, ISBN 978-3-319-28239-8, (2016), Springer International Publishing
  book chapter
• KUREŠ, M.:
  On fixed point subalgebras of some local algebras over a field, Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova
  journal article in Scopus
• DOUPOVEC, M.; KUREŠ, M.:
  Some geometric constructions on Frobenius Weil bundles, Elsevier
  journal article in Web of Science
• KUREŠ, M.:
  Jet theory in microstructures, Thomas Wohlbier, TTP USA, t.wohlbier@ttp.net
  journal article in Web of Science
• KUREŠ, M.:
  Weil algebras associated to functors of third order semiholonomic velocities,
  Mathematical Journal of Okayama University, Vol.56, (2014), No.1, pp.117-127, ISSN 0030-1566, Okayama University
  journal article - other
• KUREŠ, M.:
  On the S-operation in polynomial rings,
  Journal of Discrete Mathematical Sciences & Cryptography, Vol.16, (2013), No.6, pp.329-336, ISSN 0972-0529, Taru Publications
  journal article - other
• KUREŠ, M.:
  Lagrangians on iterated tangent bundles and the Hamiltonization,
  Miskolc Mathematical Notes, Vol.14, (2013), No.2, pp.525-538, ISSN 1787-2405, Institute of Mathematics, University of Miskolc
  journal article - other
• KUREŠ, M.:
  Fixed point subalgebras of Weil algebras: from geometric to algebraic questions,
  Complex and Differential Geometry, pp.183-192, ISBN 978-3-642-20299-5, (2011), Springer
  conference paper
  akce: Complex and Differential Geometry, Hannover, 14.09.2009-18.09.2009
• KUREŠ, M.; SKULA, L.:
  Reduction of matrices over orders of imaginary quadratic field,
  LINEAR ALGEBRA AND ITS APPLICATIONS, Vol.435, (2011), No.6, pp.1903-1919, ISSN 0024-3795, Elsevier
  journal article - other

List of publications at Portal BUT

Abstracts of most important papers:

• KUREŠ, M.; SKULA, L.:
  Reduction of matrices over orders of imaginary quadratic field,
  LINEAR ALGEBRA AND ITS APPLICATIONS, Vol.435, (2011), No.6, pp.1903-1919, ISSN 0024-3795, Elsevier
  journal article - other
  A special decomposition (called the near standard form) of (1,2)-matrices over a ring is introduced and a method for a reduction of such matrices is explained. This can be applied for a detection of elementary second order matrices among invertible second order matrices. The tool is used in detail over orders of imaginary quadratic fields, where an algorithm, a number of properties and examples are presented.
• KUREŠ, M.:
  Local approach to higher order contact elements,
  Reports on Mathematical Physics, Vol.58, (2006), No.2, pp.393-409, ISSN 0034-4877, Elsevier
  journal article - other
  Local description of regular velocities and contact elements including algebraic geometry view.
• KUREŠ, M.:
  Weil modules and gauge bundles,
  Acta Mathematica Sinica, Vol.22, (2006), No.1, pp.271-278, ISSN 1439-8516
  journal article - other
  Finite dimensional modules over Weil algebras are investigated and corresponding gauge bundle functors from the category of vector bundles into the category of fibered manifolds are determined. The equivalence of two definitions of gauge Weil functors is proved and a number of geometric examples is presented, including a new description of vertical Weil bundles.
• KUREŠ, M., MIKULSKI, W.:
  Natural operators lifting vector fields to bundles of Weil contact elements,
  Czechoslovak Mathematical Journal, Vol.54 (129), (2004), No.6, pp.855-866
  journal article - other
  The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K^A of Weil contact elements and the subalgebra of fixed points SA of the Weil algebra A is determined.
• KUREŠ, M.:
  Generalizations of jets and reflections in the theory of connections,
  Publicationes Mathematicae, Maďarsko, Vol.59, (2001), No.3-4, pp.339-352
  journal article - other
  Classical holonomic jets are generalized to nonholonomic jets and furthermore, to quasijets, which are in fact certain vector bundle morphisms. Higher order connections are viewed as sections of r-th order jet prolongation of a fibered manifold. This approach is prolonged to quasijets and obtained quasiconnections are studied.