Prof. RNDr. Olga Rossi, DrSc.
formerly Krupková, maiden name Štěpánková

Olga Rossi's photo

Publications

Books

  1. O. Krupková, The Geometry of Ordinary Variational Equations, Lecture Notes in Mathematics 1678 (Springer, Berlin, 1997) 251 pp., ISBN 3-540-63832-6
  2. D. Krupka and O. Krupková, Topology and Geometry (SPN, Praha, 1989) 404 pp. (in Czech)

Edited Books

  1. O. Krupková and D. J. Saunders (Eds.), Variations, Geometry and Physics, Volume in honour of D. Krupka’s 65th birthday (Nova Science Publishers, New York, 2009) 360 pp., ISBN 978-1-60456-920-9
  2. O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.), Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007 (World Scientific, Singapore, 2008) 717 pp., ISBN-13 978-981-279-060-6, 10 981-279-060-8
  3. K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), Global Analysis and Applied Mathematics, AIP Conf. Proc. 729 (American Institute of Physics, New York, 2004) 398 pp., ISBN 0-7354-0209-4

Book Chapters

  1. O. Rossi, Lepage Manifolds, In: Lie Groups, Differential Equations, and Geometry, Springer, 2017
  2. O. Krupková, Variational Equations on Manifolds, In: Advances in Mathematics Research, Vol. 9 (Nova Science Publishers, New York, 2009) 201-274, ISBN 978-1-60692-179-1
  3. O. Krupková, Lepage Forms in the Calculus of Variations, In: Variations, Geometry and Physics, Volume in honour of D. Krupka’s 65th birthday (Nova Science Publishers, New York, 2009) 29-56, ISBN 978-1-60456-920-9
  4. O. Krupková and G. E. Prince, Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations, In: Handbook of Global Analysis (Elsevier, 2008) 841-908, ISBN 978-0-444-52833-9
  5. O. Krupková, Helmholtz conditions in the geometry of second order ordinary differential equations, In: Differential Geometric Methods in Mechanics and Field Theory, Volume in Honour of W. Sarlet (Academia Press, Gent, 2007) 91-114, ISBN 978-90-382-1128-2
  6. O. Krupková, Differential systems in higher-order mechanics. In: Proceedings of the Seminar on Differential Geometry, Mathematical Publications 2 (Silesian University, Opava 2000) 87-130, ISBN 80-7248-104-5
  7. O. Krupková, A new look at Dirac’s theory of constrained systems, In: Gravity, Particles and Space-Time, Volume in Honour of D. Ivanenko (World Scientific, Singapore, 1996), 507-518, ISBN 981-02-2668-3

Papers

  1. O. Rossi, Geometry of variational partial differential equations and Hamiltonian systems, in: Geometry of Jets and Fields, Proc. Conf. Bedlewo, Poland, May 2015 (Banach Center Publications, Vol. 110, 2016)
  2. D. Barseghyan and O. Rossi, On a class of Schrödinger operators exhibiting spectral transition, in: Functional Analysis and Operator Theory for Quantum Physics, Volume in honor of P. Exner, J. Dittrich and A. Laptev (Eds.) (EMS Publishing House, 2017, pp. 55-69)
  3. D. J. Barrett, R. Biggs, C. C. Remsing and O. Rossi, Invariant nonholonomic Riemannian structures on three-dimensional Lie groups, J. Geom. Mech. 8 (2016) 139-168
  4. O. Rossi, G. E. Prince and D. J. Saunders, Shape maps for partial differential equations J. Math. Pures Appl., DOI:10.10116/j.matpur.2016.07.010
  5. M. Palese, O. Rossi, E. Winterroth and J. Musilová, Variational sequences, representation sequences and applications in physics, SIGMA 12 (2016), 045, 45 pages
  6. D. J. Saunders, O. Rossi and G. E. Prince, Tangent bundle geometry induced by second order partial differential equations, J. Math. Pures Appl. 106 (2016), 296-318
  7. O. Rossi and D. J. Saunders, Lagrangian and Hamiltonian duality, J. Math. Sci. (Springer) 218 (2016), 813-819
  8. O. Rossi and D. J. Saunders, Dual jet bundles, Hamiltonian systems and connections, Diff. Geom. Appl. 35 (2014) 178-198
  9. O. Rossi, Homogeneous differential equations and the inverse problem of the calculus of variations, Publ. Math. Debrecen 84 (2014) 165-188
  10. O. Rossi, Homogeneous differential equations and the inverse problem of the calculus of variations, Report No.19, ISRN IML-R-19-12/13-SE+spring, Institut Mittag-Leffler, Stockholm, 2013, 19pp.
  11. O. Rossi and J. Musilová, On the inverse variational problem in nonholonomic mechanics, Commun. Math. 20 (2012) 41-62
  12. O. Rossi and J. Musilová, The relativistic mechanics in a nonholonomic setting: a unified approach to particles with non-zero mass and massless particles, J. Phys. A: Math. Theor. 45 (2012) 255202, DOI: 10.1088/1751-8113/45/25/255202
  13. O. Krupková, Nonconservative mechanical systems with nonholonomic constraints, Science China: Physics, Mechanics and Astronomy 55 (2012) 1475-1484
  14. D. Krupka, O. Krupková and D. J. Saunders, Cartan-Lepage forms in geometric mechanics, Int. J. Nonlin. Mechanics 47 (2012) 1154-1160
  15. R. Paláček and O. Krupková, On the Zermelo problem in Riemannian manifolds, Balkan J. Geom. Appl. 17 (2) (2012) 65-69
  16. W. Sarlet, G. Prince, T. J. Mestdag and O. Krupková, Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type, J. Phys. A: Math. Theor. 45 (2012) 085208, DOI: 10.1088/1751-8113/45/8/085208
  17. O. Krupková and D. J. Saunders, Affine duality, and Lagrangian and Hamiltonian systems, Int. J. Geom. Met. Mod. Phys. 8 (3) (2011) 669-697, DOI: 10.1142/S0219887811005336
  18. O. Krupková, Geometric mechanics on nonholonomic submanifolds, Commun. Math. 18 (1) (2010) 51-77
  19. O. Krupková and R. Malíková, Helmholtz conditions and their generalizations, Balkan J. Geom. Appl. 15 (1) (2010) 80-89
  20. D. Krupka, O. Krupková and D. J. Saunders, The Cartan form and its generalizations in the calculus of variations, Int. J. Geom. Met. Mod. Phys. 7 (4) (2010) 631-654, DOI: 10.1142/S0219887810004488
  21. O. Krupková, The nonholonomic variational principle, J. Phys. A: Math. Theor. 42 (2009) 185201 (40 pp.) DOI:10.1088/1751-8113/42/18/185201
  22. O. Krupková, Noether Theorem, 90 years on, In: Geometry and Physics, Proc. XVII International Fall Workshop on Geometry and Physics, Castro Urdiales, Spain, 2008, AIP Conf. Proceedings (American Institute of Physics, New York, 2009), 159-170
  23. O. Krupková and J. Musilová, Nonholonomic forces and the Mach Principle in the Special Relativity Theory, In: Ernst Mach: Physics-Philosophy-Education, Proc. Conf. in honour of Ernst Mach’s 170th birthday, Brno, Czech Republic, 2008 (Masaryk University, Brno, 2009) (in Czech), 123-126
  24. O. Krupková and D. Smetanová, Lepage equivalents of second order Euler-Lagrange forms and the inverse problem of the calculus of variations, J. Nonlin. Math. Phys. 16 (2009) 1-16
  25. O. Krupková, Variational Equations on Manifolds, Expert Commentary, In: Advances in Mathematics Research, Vol. 9 (Nova Science Publishers, New York, 2009) 295-299, ISBN 978-1-60692-179-1
  26. O. Krupková, J. Volná and P. Volný, Constrained Lepage forms, In: Differential Geometry and its Applications, Proc. 10th Int. Conf. on Diff. Geom. & Appl., Olomouc, August 2007, O. Kowalski, D. Krupka, O. Krupková and J. Slovák (Eds.) (World Scientific, Singapore, 2008) 627-633, ISBN-13 978-981-279-060-6, ISBN-10 981-279-060-8
  27. D. Krupka and O. Krupková, Contact symmetries and variational PDE’s, Acta Appl. Math. 101 (1–3) (2008), A special issue dedicated to the 60th anniversary of Valentin Lychagin, 163-176
  28. O. Krupková and G. E. Prince, Lepage forms, closed two-forms and second order ordinary differential equations, Russ. Math. (Izv. VUZ) 51 (12) (2007), N. I. Lobachevskii Anniversary Volume, 1-16
  29. O. Krupková, Variational exterior differential systems, In: Symmetry and Perturbation Theory, Proc. Int. Conf. SPT, Otranto, June 2007, G. Gaeta, R. Vitolo and S. Walcher (Eds.) (World Scientific, Singapore, 2007) 124-131, ISBN 978-981-277-616-7, 981-277-616-8
  30. D. Krupka, O. Krupková, G. Prince and W. Sarlet, Contact symmetries of the Helmholtz form, Diff. Geom. Appl. 25 (2007) 518-542
  31. O. Krupková, The canonical distribution in nonholonomic mechanics and field theory, In: Proc. of the XV International Workshop on Geometry and Physics, Puerto de la Cruz, Tenerife, Canary Islands, Spain, September 2006, D. Iglesias Ponte, J. C. Marrero González, F. Matín Cabrera, E. Padrón Fernández and D. Sosa Martín (Eds.), Publ. de la RSME 11 (Real Sociedad Matemática Espanola, Madrid, 2007) 167-176, ISBN 978-84-935196-1-2
  32. O. Krupková and J. Musilová, Non-holonomic relativistic mechanics: A unified approach to particles with non-zero mass and massless particles, Preprint Series in Global Analysis and Applications 7/2006 (Dept. of Algebra and Geometry, Palacký University, Olomouc) 13 pp.
  33. O. Krupková and P. Volný, Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems, Lobachevskii J. Math. 23 (2006) 95-150
  34. O. Krupková, Partial differential equations with differential constraints, J. Diff. Eq. 220 (2006) 354-395
  35. O. Krupková and P. Volný, Euler-Lagrange and Hamilton equations for non-holonomic systems in field theory, J. Phys. A: Math. Gen. 38 (2005) 871-874
  36. O. Krupková and M. Swaczyna, Horizontal and contact forms on constraint manifolds, Rend. Circ. Mat. Palermo, Serie II, Suppl. 75 (2005) 259-267
  37. O. Krupková and J. Musilová, Non-holonomic variational systems, Rep. Math. Phys. 55 (2005) 211-220
  38. D. Krupka, O. Krupková, G. E. Prince and W. Sarlet, Contact symmetries and variational sequences, In: Proc. 9th Int. Conf. on Diff. Geom. & Appl., J. Bureš, O. Kowalski, D. Krupka and J. Slovák (Eds.), Prague, August 2004 (Charles University, Prague, 2005) 605-615
  39. O. Krupková, The geometry of variational equations, In: Global Analysis and Applied Mathematics, K. Tas, D. Krupka, O. Krupková and D. Baleanu (Eds.), AIP Conference Proceedings 729 (American Institute of Physics, 2004) 19-38, ISBN 0-7354-0209-4
  40. O. Krupková, Variational metric structures, Publ. Math. Debrecen 62 (2003), Issue in honour of L. Tamássy, 461-495
  41. A. Haková and O. Krupková, Variational first-order partial differential equations, J. Diff. Eq. 191 (2003) 67-89
  42. O. Krupková, Non-variational Hamiltonian structures, Anal. Univ. “Al. I. Cuza” Iași, Ser. Matematica 49 (2) (2003), Issue in honour of R. Miron, 266-288
  43. P. Volný and O. Krupková, Hamilton equations for non-holonomic mechanical systems, In: Differetial Geometry and its Applications, Proc. Conf., Opava 2001 (Mathematical Publications 3, Silesian University, Opava, 2003) 369-380, ISBN 80-7248-166-5
  44. O. Krupková and J. Musilová, Constraint Helmholtz conditions, Preprint 6/2002 GAČR 201/00/0724 (Inst. of Theoretical Physics and Astrophysics, Masaryk University, Brno, 2002) 10 pp.
  45. O. Krupková and M. Swaczyna, The non-holonomic variational principle, Preprint 8/2002 GAČR 201/00/0724 (Inst. of Theoretical Physics and Astrophysics, Masaryk University, Brno, 2002) 34 pp.
  46. O. Krupková, Recent results in the geometry of constrained systems, Rep. Math. Phys. 49 (2002) 269-278
  47. O. Krupková, Hamiltonian field theory, J. Geom. Phys. 43 (2002) 93-132
  48. O. Krupková and D. Smetanová, Legendre transformation for regularizable Lagrangians in field theory, Lett. Math. Phys. 58 (2001) 189-204
  49. O. Krupková and D. Smetanová, On regularization of variational problems in first order field theory, Rend. Circ. Mat. Palermo, Serie II, Suppl. 66 (2001) 133-140
  50. O. Krupková, Hamiltonian field theory revisited: A geometric approach to regularity, In: Steps in Differential Geometry, Proc. Colloq. Diff. Geom., Debrecen, July 2000, L. Kozma, P. T. Nagy and L. Tamássy (Eds.) (Debrecen University, Debrecen, 2001) 187-207
  51. O. Krupková and J. Musilová, The relativistic particle as a mechanical system with non-holonomic constraints, J. Phys. A: Math. Gen. 34 (2001) 3859-3876
  52. O. Krupková, Higher-order mechanical systems with constraints, J. Math. Phys. 41 (2000) 5304-5324
  53. O. Krupková, On the geometry of non-holonomic mechanical systems, In: Differential Geometry and Applications, Proc. Conf., Brno, August 1998, I. Kolář, O. Kowalski, D. Krupka and J. Slovák (Eds.) (Masaryk University, Brno, 1999) 533-546, ISBN 80-210-2097-0, Electronic edition: EMIS
  54. J. Musilová, O. Krupková and D. Krupka, The variational sequence in Physics (in Czech), Čs. čas. fyz. A 48 (1998), Issue in honour of M. Černohorský, 329-341
  55. O. Krupková, Mechanical systems with non-holonomic constraints, J. Math. Phys. 38 (1997) 5098-5126
  56. O. Krupková, Noether theorem and first integrals of constrained Lagrangean systems, Math. Bohemica 122 (1997) 257-265
  57. O. Krupková, Symmetries and first integrals of time-dependent higher-order constrained systems, J. Geom. Phys. 18 (1996) 38-58
  58. O. Krupková, Higher-order constrained systems on fibered manifolds: An exterior differential systems approach, In: New Developments in Differential Geometry, Proc. Colloq. on Diff. Geom., Debrecen, 1994, L. Tamássy and J. Szenthe (Eds.) (Kluwer, Dordrecht, 1996) 255-278, ISBN 0-7923-3822-7
  59. O. Krupková, A geometric setting for higher-order Dirac-Bergmann theory of constraints, J. Math. Phys. 35 (1994) 6557-6576
  60. O. Krupková, Variational metrics on R × TM and the geometry of nonconservative mechanics, Math. Slovaca 44 (1994) 315-335
  61. O. Krupková, On the inverse problem of the calculus of variations for ordinary differential equations, Math. Bohemica 118 (1993) 261-276
  62. O. Krupková and A. Vondra, On some integration methods for connections on fibered manifolds, In: Differential Geometry and Its Applications, Proc. Conf., Opava, August 1992, O. Kowalski and D. Krupka (Eds.) (Math. Publications 1, Silesian University, Opava, Czechoslovakia, 1993) 89-102, ISBN 80-901581-0-2
  63. O. Krupková, Liouville and Jacobi theorems for vector distributions, In: Differential Geometry and Its Applications, Proc. Conf., Opava, August 1992, O. Kowalski and D. Krupka (Eds.) (Math. Publications 1, Silesian University, Opava, Czechoslovakia, 1993) 75-88, ISBN 80-901581-0-2
  64. O. Krupková, Hamilton-Jacobi distributions, Preprint (J. E. Purkyně University Brno, 1990) 40 pp.
  65. O. Krupková, A note on the Helmholtz conditions, In: Differential Geometry and Its Applications, Proc. Conf., Brno, August 1986, Communications, D. Krupka and A. Švec (Eds.) (J. E. Purkyně University, Brno, Czechoslovakia, 1987) 181-188
  66. O. Krupková, Lepagean 2-forms in higher order Hamiltonian mechanics, II. Inverse problem, Arch. Math. (Brno) 23 (1987) 155-170
  67. O. Krupková, Lepagean 2-forms in higher order Hamiltonian mechanics, I. Regularity, Arch. Math. (Brno) 22 (1986) 97-120
  68. M. Štefanová and O. Štěpánková, Variationality and invariance of systems of partial differential equations, Scripta Fac. Sci. Nat. UJEP Brunensis (Physica) 5 (1985) 283-288
  69. O. Štěpánková, The local inverse problem of the calculus of variations in higher order Hamiltonian mechanics, In: Geometrical Methods in Physics, Proc. Conf. on Diff. Geom. And Appl., Nové Město na Moravě, September 1983, Part 2, D. Krupka (Ed.) (J. E. Purkyně University, Brno, Czechoslovakia, 1984) 275-287
  70. D. Krupka and O. Štěpánková, On the Hamilton form in second order calculus of variations, In: Geometry and Physics, Proc. Internat. Meeting, Florence, 1982, M. Modugno (Ed.) (Pitagora, Bologna, 1983) 85-102, ISBN 88-371-0280-1
  71. O. Štěpánková, Generalized regularity in Hamiltonian mechanics (in Czech), Charles University, Prague, March 1984, 29 pp.; paper won a prize at the Czechoslovak Students’ Scientific Conference, Prague, 1984
  72. M. Štefanová and O. Štěpánková, Invariance of motion equations and variationality conditions (in Czech), Charles University, Prague, March 1982; paper won a prize at the Czechoslovak Students’ Scientific Conference, Prague, 1982

Dissertations

  1. O. Krupková, Geometry of Lepagean 2-forms, DrSc. Thesis (Silesian University, Opava & Masaryk University, Brno) 1997
  2. O. Krupková, A Geometric Theory of Variational Ordinary Differential Equations, Habilitation Thesis (Silesian University, Opava & Masaryk University, Brno, 1995) 165 pp.
  3. O. Krupková, Variational Analysis on Fibered Manifolds over One-dimensional Bases, PhD Thesis (Silesian University, Opava & Charles University, Prague, 1992) 67 pp.
  4. O. Štěpánková, The inverse variational problem in mechanics (in Czech), MSc. Thesis (Charles University, Prague, May 1984) 63 pp.

University Textbooks

  1. O. Krupková, Lineární algebra 1, Univerzita Palackého, Olomouc, 2008
  2. O. Krupková, Moderní metody matematiky: Analýza, topologie a geometrie, Ostravská univerzita, Ostrava, 2006
  3. O. Krupková, Variační počet na varietách, Ostravská univerzita, Ostrava, 2006   pdf
  4. O. Krupková and M. Swaczyna, Variační počet, Ostravská univerzita, Ostrava, 2006   pdf
  5. O. Krupková, Matematická analýza 4, Integrální počet, Ostravská univerzita, Ostrava, 2006
  6. O. Krupková, Matematika 3, Diferenciální počet funkcí více proměnných, Ostravská univerzita, Ostrava, 2004
  7. O. Krupková, Lineární a multilineární algebra, vybrané kapitoly, pomocné učební texty, MÚ SU, Opava, 1999, 2000
  8. O. Krupková, Vektorové distribuce, pomocný učební text, PřF Brno, 1990
  9. O. Krupková, Řešené úlohy z topologie a geometrie, pomocný učební text, PřF MU Brno, 1986, 276 s.


Last modified: Fri Dec 16 13:45:22 CET 2016