| 1. | L.F.Blazhyevskyi, V.Kovalchuk |
| About taking into account relativistic corrections for
a resonant atomic interaction
Lviv University Bulletin, 30, pp. 6-8, 1998. |
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| Abstract | |
| 2. | V.Kovalchuk |
| About relativistic attraction forces influence upon the thermodynamic
characteristics of atomic hydrogen and inert gases
Lviv University Bulletin, 31, pp. 47-51, 1998. |
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| Abstract | |
| 3. | J.J.Sławianowski, V.Kovalchuk |
| Klein-Gordon-Dirac equation: physical justification and quantization attempts
Reports on Mathematical Physics, 49, 2/3, pp. 249-257, 2002. |
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| Abstract Full text | |
| 4. | J.J.Sławianowski, V.Kovalchuk |
| Invariant geodetic problems on the affine group and related Hamiltonian systems
Reports on Mathematical Physics, 51, 2/3, pp. 371-379, 2003. |
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| Abstract Full text | |
| 5. | J.J.Sławianowski, V.Kovalchuk |
| Invariant geodetic problems on the projective group Pr(n,R)
Proceedings of Institute of Mathematics of NAS of Ukraine, editors: A.G.Nikitin, V.M.Boyko, R.O.Popovych, and I.A.Yehorchenko, 50, part 2, pp. 955-960, Kyiv, Institute of Mathematics, 2004. |
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| Abstract Full text | |
| 6. | V.Kovalchuk |
| Green function for Klein-Gordon-Dirac equation
Journal of Nonlinear Mathematical Physics, 11, Supplement, pp. 72-77, 2004. |
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| Abstract Full text | |
| 7. | J.J.Sławianowski, V.Kovalchuk |
| Classical and quantized affine physics. A step towards it
Journal of Nonlinear Mathematical Physics, 11, Supplement, pp. 157-166, 2004. |
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| Abstract Full text | |
| 8. | J.J.Sławianowski, V.Kovalchuk, A.Sławianowska, B.Gołubowska, A.Martens, E.E.Rożko, Z.J.Zawistowski |
| Invariant geodetic systems on Lie groups and affine models of internal and collective
degrees of freedom
Prace IPPT - IFTR Reports, 7, 2004, 164 p. |
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| Full text | |
| 9. | J.J.Sławianowski, V.Kovalchuk, A.Sławianowska, B.Gołubowska, A.Martens, E.E.Rożko, Z.J.Zawistowski |
| Affine symmetry in mechanics of collective and internal modes. Part
I. Classical models
Reports on Mathematical Physics, 54, 3, pp. 373-427, 2004; arXiv:0802.3027. |
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| Abstract | |
| 10. | J.J.Sławianowski, V.Kovalchuk, A.Sławianowska, B.Gołubowska, A.Martens, E.E.Rożko, Z.J.Zawistowski |
| Affine symmetry in mechanics of collective and internal modes. Part
II. Quantum models
Reports on Mathematical Physics, 55, 1, pp. 1-45, 2005; arXiv:0802.3028. |
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| Abstract | |
| 11. | J.J.Sławianowski, V.Kovalchuk, B.Gołubowska, A.Martens, E.E.Rożko |
| Dynamical systems with internal degrees of freedom in non-Euclidean spaces
Prace IPPT - IFTR Reports, 8, 2006, 129 p.; arXiv:0802.3115. |
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| Full text | |
| 12. | J.J.Sławianowski, V.Kovalchuk |
| Search for the geometrodynamical gauge group. Hypotheses and some results
Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization (June 8-13, 2007, Sts. Constantine and Elena, Bulgaria), Ed. Ivailo M. Mladenov, SOFTEX, Sofia, 2008, pp. 66-132. |
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| Abstract | |
| 13. | V.Kovalchuk, J.J.Sławianowski |
| Hamiltonian systems inspired by the Schrödinger equation
Proceedings of the Seventh International Conference on Symmetry in Nonlinear Mathematical Physics (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), 4, 046, 9 pages, 2008; arXiv:0805.4024. |
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| Abstract Full text | |
| 14a. | V.Kovalchuk, E.E.Rożko |
| Classical models of affinely-rigid bodies with "thickness" in degenerate dimension
Journal of Geometry and Symmetry in Physics, 14, pp. 51-65, 2009; arXiv:0902.3573. |
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| Abstract | |
| 14b. | reprinted in: Proceedings of the Tenth International Conference on Geometry, Integrability and Quantization (June 6-11, 2008, Sts. Constantine and Elena, Bulgaria), Eds. Ivailo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, Avangard Prima, Sofia, 2009, pp. 197-210. |
| Abstract | |
| 15. | J.J.Sławianowski, V.Kovalchuk |
| Symmetries and geometrically implied nonlinearities in mechanics and field theory
in: "Problems of stability and stabilization of motion", Eds. S.Ja.Stepanov and A.A.Burov, Bulletin of Computing Centre named after A.A.Dorodnitsyn, Russian Academy of Sciences, Moscow, 2009, pp. 119-150 (in Russian); arXiv:0911.3818. |
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| Abstract Full text | |
| 16. | J.J.Sławianowski, V.Kovalchuk |
| Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors
and new ideas of nonlinearity in quantum mechanics
Reports on Mathematical Physics, 65, 1, pp. 29-76, 2010; arXiv:0812.5055. |
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| Abstract | |
| 17. | J.J.Sławianowski, V.Kovalchuk, B.Gołubowska, A.Martens, E.E.Rożko |
| Quantized excitations of internal affine modes and their influence on Raman spectra
Acta Physica Polonica B, 41, 1, pp. 165-218, 2010; arXiv:0901.0243. |
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| Abstract | |
| 18. | V.Kovalchuk |
| On classical dynamics of affinely-rigid bodies subject to the Kirchhoff-Love constraints
Proceedings of the Eighth International Conference on Symmetry in Nonlinear Mathematical Physics (June 21-27, 2009, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), 6, 031, 12 pages, 2010; arXiv:1004.1248. |
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| Abstract Full text | |
| 19. | J.J.Sławianowski, V.Kovalchuk, A.Martens, B.Gołubowska, E.E.Rożko |
| Quasiclassical and quantum systems of angular momentum. Part I. Group algebras as a framework for
quantum-mechanical models with symmetries
Journal of Geometry and Symmetry in Physics, 21, pp. 61-94, 2011; arXiv:1007.4121. |
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| Abstract | |
| 20. | J.J.Sławianowski, V.Kovalchuk, A.Martens, B.Gołubowska, E.E.Rożko |
| Quasiclassical and quantum systems of angular momentum. Part II. Quantum mechanics on Lie groups and
methods of group algebras
Journal of Geometry and Symmetry in Physics, 22, pp. 67-94, 2011; arXiv:1008.0512. |
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| Abstract | |
| 21. | J.J.Sławianowski, V.Kovalchuk, A.Martens, B.Gołubowska, E.E.Rożko |
| Quasiclassical and quantum systems of angular momentum. Part III. Group algebra su(2), quantum angular
momentum and quasiclassical asymptotics
Journal of Geometry and Symmetry in Physics, 23, pp. 59-95, 2011; arXiv:1008.3074. |
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| Abstract | |
| 22. | J.J.Sławianowski, V.Kovalchuk, A.Martens, B.Gołubowska, E.E.Rożko |
| Quasiclassical and quantum dynamics of systems of angular momenta
Proceedings of the Twelfth International Conference on Geometry, Integrability and Quantization (June 4-9, 2010, Sts. Constantine and Elena, Bulgaria), Eds. Ivailo M. Mladenov, Gaetano Vilasi and Akira Yoshioka, Avangard Prima, Sofia, 2011, pp. 70-155. |
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| Abstract | |
| 23. | J.J.Sławianowski, V.Kovalchuk, A.Martens, B.Gołubowska, E.E.Rożko |
| Mechanics of systems of affine bodies. Geometric foundations and applications in dynamics of structured media
Mathematical Methods in the Applied Sciences, 34, pp. 1512-1540, 2011; arXiv:1010.3333. |
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| 24. | J.J.Sławianowski, V.Kovalchuk, A.Martens, B.Gołubowska, E.E.Rożko |
| Essential nonlinearity implied by symmetry group. Problems of affine invariance in mechanics and physics
in: "Analytical and Geometrical Problems in Continuum Mechanics", a special issue of Discrete and Continuous Dynamical Systems - Series B, 17, 2, pp. 699-733, 2012. |
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| 25. | J.J.Sławianowski, V.Kovalchuk, A.Martens, B.Gołubowska, E.E.Rożko |
| Generalized Weyl-Wigner-Moyal formalism and topological groups
Mathematical Methods in the Applied Sciences, 35, pp. 17-42, 2012; arXiv:1012.5768. |
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| 26. | J.J.Sławianowski, B.Gołubowska, E.E.Rożko, V.Kovalchuk, E.Gobcewicz |
| Affine bodies revisited. Constraints, symmetry, analytical methods and some perspectives
arXiv:1012.4926. |
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| 27. | A.Popov, V.Kovalchuk |
| Parametric representation of wave propagation in nonuniform media (both in transmission and stop bands)
arXiv:1112.1199. |