Publications

The recent publication record of members of the LRI includes:

2017

  • D. Krupka, Z. Urban, and J. Volna, Variational submanifolds of Euclidean spaces, submitted.

2016

  • G. Sardanashvily, Noether's Theorems, Applications in Mechanics and Field Theory, Atlantis Studies in Variational Geometry, Vol. 3, Atlantis Press, Amsterdam-Beijing-Paris, 2016.
  • N. Voicu, Energy–momentum tensors in classical field theories - A modern perspective, Int. J. Geom. Meth. Mod. Phys. (2016) in print.
  • Z. Urban and J. Volna, The metrizability problem for Lorentz-invariant affine connections, Int. J. Geom. Meth. Mod. Phys. (2016) to appear; DOI: 10.1142/S0219887816501103
  • A.V. Zhuchok and M. Demko, Free n-dinilpotent doppelsemigroups, in: Algebra and Discrete Mathematics, Vol. 22, no. 2 (2016), pp. 304-316.

2015

  • A.M. Bloch, D. Krupka, and D.V. Zenkov, The Helmholtz Conditions and the Method of Controlled Lagrangians, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 1-29.
  • D. Krupka, The Sonin-Douglas Problem, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 31-73.
  • J. Volná and Z. Urban, First-order Variational Sequences in Field Theory, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 215-284.
  • R. Matsyuk, Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 75-102.
  • N. Voicu, Source Forms and Their Variational Completions, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 171-214.
  • Z. Urban, Variational Principles for Immersed Submanifolds, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Atlantis Press, Amsterdam-Beijing-Paris, 2015, pp. 103-170.
  • J. Volna and Z. Urban, The interior Euler-Lagrange operator in field theory, Math. Slovaca 65, No. 6 (2015) 1427-1444.
    DOI: 10.1515/ms-2015-0097
  • N. Voicu and D. Krupka, Canonical variational completions of differential systems, J. Math. Phys. 56, 043507 (2015); arXiv:1406.6646 [math-ph].  
  • D. KrupkaG. MorenoZ. UrbanJ. Volná, On a bicomplex induced by the variational sequence, Int. J. Geom. Meth. Mod. Phys. 12, No. 5 (2015) 1550057 (15 pp.) DOI: 10.1142/S0219887815500577
  • G. Moreno and M.E. Stypa, Natural boundary conditions in geometric calculus of variations, Math. Slovaca 65, No. 6 (2015), 1531-1556, DOI: 10.1515/ms-2015-0105
  • Z. Urban and D. Krupka, Variational theory on Grassmann fibrations: Examples, Acta Math. Acad. Paed. Nyíregyhasiensis 31, No. 1 (2015) 153-170.  pdf
  • D. Krupka, Invariant variational structures on fibered manifolds, Int. J. Geom. Met. Mod. Phys. 12, No. 2 (2015) 1550020.
  • D. Krupka, Introduction to Global Variational Geometry, Atlantis Studies in Variational Geometry, Vol. 1, Atlantis Press, Amsterdam-Beijing-Paris, 2015.

2014

  • Z. Urban and D. Krupka, Foundations of higher-order variational theory on Grassmann fibrations, Int. J. Geom. Met. Mod. Phys. 11, No. 7 (2014) 1460023 (27 pp.) doi 
  • N. Voicu, Biharmonic maps from Finsler spacesPublicationes Mathematicae Debrecen 84, No. 3-4 (2014). 
  • J. Brajercik, M. Demko and D. Krupka, Principal bundle structure on jet prolongations of frame bundles, Math. Slovaca 64, No. 5 (2014) 1277-1290.
  • J. Brajercik and M. Demko, On sheaf spaces of partially ordered quasigroups, Quasigroups and Related Systems 22 (2014) 51-58.

  • D. Krupka, Lepage forms in Kawaguchi spaces and the Hilbert form, paper in honor of Professor Lajos Tamassy, Publ. Math. Debrecen 84, No. 1-2 (2014) 147-164.

2013

  • J. Brajercik and M. Demko, Second order natural Lagrangians on coframe bundles, Miskolc Mathematical Notes 14, No. 2 (2013), 487-494.  pdf
  • D. Krupka, Z. Urban and J. Volna, Variational projectors in fibred manifolds, Miskolc Mathematical Notes 14, No. 2 (2013), 503-516.  pdf
  • E. Tanaka and D. Krupka, On the structure of Finsler and Areal spaces, Miskolc Mathematical Notes 14, No. 2 (2013), 539-546.  pdf
  • Z. Urban and D. Krupka, The Helmholtz conditions for systems of second order homogeneous differential equations, Publ. Math. Debrecen (2013), 83, No. 1-2 (2013) 71-84.
  • T. Li and D. Krupka, The geometry of tangent bundles: Canonical vector fields, Geometry (2013), Hindawi Publishing Corporation, Article ID 364301, 10 pp.  doi-pdf
  • Z. Urban and D. Krupka, The Zermelo conditions and higher order homogeneous functions, Publ. Math. Debrecen 82, No. 1 (2013) 59-76.

2012

  • M. Demko, Partially ordered quasigroups, Southeast Asian Bulletin of Mathematics 36 (5), (2012), 631–649. 
  • Z. Urban and D. Krupka, Variational sequences on fibred velocity spaces, Glob. J. Math. Sci. 1, No. 1, 6th World Congress of Nonlinear Analysts, June 25-July 1, 2012 Athens, Greece (2012) 77-87. 
  • E. Tanaka and D. Krupka, On metrizability of invariant affine connections, Internat. J. Geom. Met. Mod. Phys. 9 (2012) 1250014 (15 pages), doi

2011

  • J. Brajercik, Invariant variational problems on principal bundles and conservation laws, Arch. Math. (Brno), 47, No. 5 (2011) 357-366.
  • J. Brajercik, Euler-Poincare reduction on frame bundles, Diff. Geom. Appl., 29 (2011) S33-S40, doi:10.1016/j.difgeo.2011.04.005. 
  • D. Krupka, O. Krupkova and D. Saunders, Cartan-Lepage forms in geometric mechanics, Internat. J. of Nonlinear Mechanics 47 (2011) 1154-1160.