Scientific Publications

 
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Scientific Journals

  1. J. Gaset, X. Gràcia, M.C. Muñoz-Lecanda, X. Rivas, N. Román-Roy.
    ``A k-contact Lagrangian formulation for nonconservative field theories''.
    Rep. Math. Phys. 87(3) (2021) 347-368.
    ( https://doi.org/10.1016/S0034-4877(21)00041-0 ).
    arXiv:2002.10458 [math-ph].
    Math. Rev. AMS MR4275665. Zbl. Math. Zbl 07371599.

  2. N. Román-Roy.
    ``An overview of the Hamilton-Jacobi Theory: The classical and geometrical approaches and some extensions and applications''.
    Mathematics 9(1) (2021) 85.
    (Special Issue New Trends in Hamilton-Jacobi Theory: Conservative and Dissipative Dynamics)
    ( https://doi.org/10.3390/math9010085 ).
    arXiv:2002.10458 [math-ph] .

  3. M. de León, J. Gaset, M. Laínz, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Higher-order contact mechanics''.
    Ann. Phys. 425 (2021) 168396.
    ( https://doi.org/10.1016/j.aop.2021.168396 ).
    arXiv:2009.12160 [math-ph].
    Math. Rev. A.M.S. MR4204371. Zbl. Math. Zbl 1457.37083.

  4. X. Gràcia, X. Rivas, N. Román-Roy,
    ``Constraint algorithm for singular field theories in the k-cosymplectic framework''.
    J. Geom. Mech. 12(1) (2020) 1-23.
    ( https://dx.doi.org/10.3934/jgm.2020002 ).
    arXiv:1812.08487 [math-ph].
    Math. Rev. A.M.S. MR4063923. Zbl. Math. Zbl 1434.70047.

  5. J. Gaset, X. Gràcia, M.C. Muñoz-Lecanda, X. Rivas, N. Román-Roy.
    ``A contact geometry framework for field theories with dissipation''.
    Ann. Phys. 414 (2020) 168092.
    ( https://doi.org/10.1016/j.aop.2020.168092 ).
    arXiv:1905.07354 [math-ph].
    Math. Rev. A.M.S. MR4067916. Zbl. Math. Zbl 1433.53042.

  6. J. Gaset, X. Gràcia, M.C. Muñoz-Lecanda, X. Rivas, N. Román-Roy.
    ``New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries''.
    Int. J. Geom. Meth. Mod. Phys. 17(6) (2020) 2050090.
    ( https://doi.org/10.1142/S0219887820500905 ).
    arXiv:1907.02947 [math-ph].
    Math. Rev. A.M.S. MR4105775.

  7. M. de León, J. Gaset, M. Laínz, X. Rivas, N. Román-Roy.
    ``Unified Lagrangian-Hamiltonian formalism for contact systems''.
    Fortschrt. Phys. 68(8) (2020) 2000045.
    ( https://doi.org/10.1002/prop.202000045 ).
    arXiv:2003.13037 [math-ph].
    Math. Rev. A.M.S. MR4156666 .

  8. S Capriotti, J Gaset, N Román-Roy, L Salomone.
    ``Griffiths variational multisymplectic formulation for Lovelock gravity''.
    Gen. Rel. Grav. 52(8) (2020) 74.
    ( https://doi.org/10.1007/s10714-020-02725-8 ).
    arXiv:1911.07278 [math-ph].
    Math. Rev. A.M.S. MR4140721. Zbl. Math. Zbl 1457.49034.

  9. N. Román-Roy.
    ``A summary on symmetries and conserved quantities of autonomous Hamiltonian systems''.
    J. Geom. Mech. 12(3) (2020) 541-551.
    ( https://doi.org/10.3934/jgm.2020009 ).
    arXiv:1806.06265 [math-ph].
    Math. Rev. A.M.S. MR4160169. Zbl. Math. Zbl 1460.37052.

  10. J. Gaset, N. Román-Roy.
    ``New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity''.
    J. Geom. Mech. 11(3) (2019) 361-396.
    ( https://dx.doi.org/10.3934/jgm.2019019 ).
    arXiv:1804.06181 [math-ph] (2018).
    Math. Rev. A.M.S. MR4026013. Zbl. Math. Zbl 1433.83005.

  11. J. Gaset, N. Román-Roy.
    ``Multisymplectic unified formalism for Einstein-Hilbert Gravity''.
    J. Math. Phys. 59(3) (2018) 032502, 39 pp.
    ( https://doi.org/10.1063/1.4998526 ).
    arXiv:1705.00569 [math-ph].
    Math. Rev. A.M.S. MR3778573. Zbl. Math. Zbl 1387.83006.

  12. A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Remarks on multisymplectic reduction''.
    Rep. Math. Phys. 81(3) (2018) 415-424.
    ( https://doi.org/10.1016/S0034-4877(18)30057-0 ).
    arXiv:1712.09901 [math-ph].
    Math. Rev. A.M.S. MR3818313. Zbl. Math. Zbl 1402.53060.

  13. M. de León, P.D. Prieto-Martínez, N. Román-Roy, S. Vilariño.
    ``Hamilton-Jacobi theory in multisymplectic classical field theories''.
    J. Math. Phys. 58(9) (2017) 092901, 36 pp.
    ( https://doi-org/10.1063/1.5004260 ).
    arXiv:1504.02020 [math-ph] (2015).
    Math. Rev. A.M.S. MR3707064. Zbl. Math. Zbl 1427.70061.

  14. J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Structural aspects of Hamilton-Jacobi theory''.
    Int. J. Geom. Meth. Mod. Phys. 13(2) (2016) 1650017 (29 pages).
    ( https://doi.org/10.1142/S0219887816500171 ).
    arXiv:1511.00288 [math-ph].
    Math. Rev. A.M.S. MR3454675. Zbl. Math. Zbl 1375.70062.

  15. J. Gaset, N. Román-Roy.
    ``Order reduction, projectability and constraints of second-order field theories and higher-order mechanics''.
    Rep. Math. Phys. 78(3) (2016) 327-337.
    ( https://doi.org/10.1016/S0034-4877(17)30012-5 ).
    arXiv:1604.02074 [math-ph].
    Math. Rev. A.M.S. MR3612742. Zbl. Math. Zbl 1384.81067.

  16. J. Gaset, P.D. Prieto-Martínez, N. Román-Roy.
    ``Variational principles and symmetries on fibered multisymplectic manifolds''.
    Comm. Math. 24(2) (2016) 137-152.
    ( https://eudml.org/doc/287890 ).
    arXiv:1705.00569 [math-ph].
    Math. Rev. A.M.S. MR3590211. Zbl. Math. Zbl 1406.49054.

  17. J.C. Marrero, M. Salgado, N. Román-Roy, S. Vilariño.
    ``Reduction of polysymplectic manifolds''.
    J. Phys. A: Math. Theor. 48(5) (2015) 055206 (43pp).
    ( https://dx.doi.org/10.1088/1751-8113/48/5/055206 ).
    arXiv:1306.0337 [math-ph].
    Math. Rev. A.M.S. MR3314697. Zbl. Math. Zbl 1321.53094.

  18. P.D. Prieto-Martínez, N. Román-Roy.
    ``A new multisymplectic unified formalism for second-order classical field theories''.
    J. Geom. Mech. 7(2) (2015) 203-253.
    ( https://dx.doi.org/10.3934/jgm.2015.7.203 ).
    arXiv:1402.4087 [math-ph].
    Math. Rev. A.M.S. MR3356592. Zbl. Math. Zbl 1372.70057.

  19. P.D. Prieto-Martínez, N. Román-Roy.
    ``Variational principles for multisymplectic second-order classical field theories''.
    Int. J. Geom. Meth. Mod. Phys. 12(8) (2015) 1560019.
    ( https://doi.org/10.1142/S0219887815600191 ).
    arXiv:1412.1451 [math-ph].
    Math. Rev. A.M.S. MR3400659. Zbl. Math. Zbl 1378.70025.

  20. L. Colombo, M. de León, P.D. Prieto-Martínez, N. Román-Roy.
    ``Geometric Hamilton-Jacobi theory for higher-order autonomous systems''.
    J. Phys. A: Math. Theor. 47(23) (2014) 235203.
    ( https://dx.doi.org/10.1088/1751-8113/47/23/235203 ).
    arXiv:1309.2166 [math-ph].
    Math. Rev. A.M.S. MR3216778. Zbl. Math. Zbl 1298.53075.

  21. L. Colombo, M. de León, P.D. Prieto-Martínez, N. Román-Roy.
    ``Unified formalism for the generalized kth-order Hamilton-Jacobi problem''.
    Int. J. Geom. Meth. Mod. Phys. 11(9) (2014) 1460037.
    ( https://dx.doi.org/10.1142/S0219887814600378 ).
    arXiv:1310.1071 [math-ph].
    Math. Rev. A.M.S. MR3270300. Zbl. Math. Zbl 1305.70039.

  22. N. Román-Roy, M. Salgado, S. Vilariño.
    ``Higher-order Noether symmetries in k-symplectic Hamiltonian field theory''.
    Int. J. Geom. Meth. Mod. Phys. 10(8) (2013) 1360013 (9 pp).
    ( https://dx.doi.org/10.1142/ S021988781360013X ).
    arXiv:0804.4785 [math-ph].
    Math. Rev. A.M.S. MR3092563.

  23. P.D. Prieto-Martínez, N. Román-Roy.
    ``Higher-order Mechanics: Variational Principles and other topics''.
    J. Geom. Mechs. 5(4) (2013) 493-510.
    ( https://arxiv.org/10.3934/jgm.2013.5.493 ).
    arXiv:1201.4102 [math-ph].
    Math. Rev. A.M.S. MR3180709. Zbl. Math. Zbl 1284.35014.

  24. A.M. Rey, N. Román-Roy, M. Salgado, S. Vilariño,
    ``k-cosymplectic classical field theories: Tulckzyjew and Skinner-Rusk formulations''.
    Math. Phys. Anal. Geom. 15(2) (2012) 1-35.
    ( https://dx.doi.org/10.1007/s11040-012-9104-z ).
    arXiv:0602038 [math-ph].
    Math. Rev. A.M.S. MR2915598. Zbl. Math. Zbl 1253.70032.

  25. P.D. Prieto-Martínez, N. Román-Roy.
    ``Unified formalism for higher-order non-autonomous dynamical systems''.
    J. Math.Phys. 53(3) (2012) 032901, 43 pp.
    ( https://dx.doi.org/10.1063/1.3692326 ).
    arXiv:1111.6020 [math-ph].
    Math. Rev. A.M.S. MR2798224. Zbl. Math. Zbl 1274.37033.

  26. A. Echeverría-Enríquez, L.A. Ibort, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Invariant forms and automorphisms of homogeneous multisymplectic manifolds''.
    J. Geom. Mech. 4(4) (2012) 397-419.
    ( https://dx.doi.org/10.3934/jgm.2012.4.397 ).
    arXiv:9805040 [math-dg].
    Math. Rev. A.M.S. MR3011894. Zbl. Math. Zbl 1266.53034.

  27. J.C. Marrero, N. Román-Roy, M. Salgado, S. Vilariño.
    ``On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory''.
    J. Math. Phys. 52(2) (2011) 022901, 20 pp.
    (
    https://dx.doi.org/10.1063/1.3545969 ).
    arXiv:1009.2703 [math-ph].
    Math. Rev. A.M.S. MR2798391 Zbl. Math. Zbl 1314.70046.

  28. N. Román-Roy, M. Salgado, S. Vilariño.
    ``SOPDES and non-linear connections''.
    Publicationes Mathematicae Debrecen 78(2) (2011) 297-316.
    ( https://dx.doi.org/10.5486/PMD.2011.4631 ).
    arXiv:1109.5830 [math-ph].
    Math. Rev. A.M.S. MR2796769. Zbl. Math. Zbl 1249.53034.

  29. N. Román-Roy, A.M. Rey, M. Salgado, S. Vilariño.
    ``On the k-symplectic, k-cosymplectic and multisymplectic formalisms of classical field theories''.
    J. Geom. Mech. 3(1) (2011) 113177.
    ( https://dx.doi.org/10.3934/jgm.2011.3.113 ).
    arXiv:0705.4364 [math-ph].
    Math. Rev. A.M.S. MR2794297. Zbl. Math. Zbl 1242.70053.

  30. P.D. Prieto-Martínez, N. Román-Roy.
    ``Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems''.
    J. Phys. A: Math. Theor. 44(40) (2011) 385203 (35 pp).
    ( https://dx.doi.org/10.1088/1751-8113/44/38/385203 ).
    arXiv:1106.3261 [math-ph].
    Math. Rev. A.M.S. MR2835156. Zbl. Math. Zbl 1242.70031.

  31. N. Román-Roy.
    ``Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories''.
    Symmetry Integrability Geom. Methods Appl. (SIGMA) 5 (2009) 100, 25 pp.
    ( https://dx.doi.org/10.3842/SIGMA.2009.100 ).
    arXiv:0506022 [math-ph].
    Math. Rev. A.M.S. MR2559661 (2010m:70028) Zbl. Math. Zbl 1241.70048.

  32. J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Geometric Hamilton-Jacobi theory for Nonholonomic Dynamical Systems''.
    Int. J. Geom. Meth. Mod. Phys. 7(3) (2010) 431-454.
    ( https://dx.doi.org/10.1142/S0219887810004385 ).
    arXiv:0908.2453 [math-ph].
    Math. Rev. A.M.S. MR2646774 (2011e:70022). Zbl. Math. Zbl 1337.70038.

  33. X. Gràcia, R. Martín, N. Román-Roy,
    ``Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories''.
    Int. J. Geom. Meth. Mod. Phys. 6(5) (2009) 851-872.
    ( https://dx.doi.org/10.3934/jgm.2011.3.113 ).
    arXiv:0903.1791 [math-ph].
    Math. Rev. A.M.S. MR2555481. Zbl. Math. Zbl 1186.53090.

  34. M. Barbero, A. Echeverría-Enríquez, D. Martín de Diego, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Unified formalism for nonautonomous mechanical systems''.
    J. Math. Phys. 49(6) (2008) 062902 (14 pp).
    ( https://dx.doi.org/10.1063/1.2929668 ).
    arXiv:0803.4085 [math-ph].
    Math. Rev. A.M.S. 2009f:37060. Zbl. Math. Zbl 1152.81326.

  35. M. Barbero, A. Echeverría-Enríquez, D. Martín de Diego, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Skinner-Rusk unified formalism for optimal control systems and applications''.
    J. Phys. A: Math. Theor. 40(40) (2007) 12071-12093.
    ( https://dx.doi.org/10.1088/1751-8113/40/40/005 ).
    arXiv:0705.2178 [math-ph].
    Math. Rev. A.M.S. 2009b:70014. Zbl. Math. Zbl 1126.70011.

  36. N. Román-Roy, M. Salgado, S. Vilariño.
    ``Symmetries and conservation laws in the Gunther k-symplectic formalism in field theory''.
    Rev. Math. Phys. 19(10) (2007) 1117-1147.
    ( https://dx.doi.org/10.1142/S0129055X07003188 ).
    arXiv:0705.4364 [math-ph].
    Math. Rev. A.M.S. 2009c:70042. Zbl. Math. Zbl 1137.70016.

  37. A. Echeverría-Enríquez, M. de León, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Extended Hamiltonian systems in multisymplectic field theories''.
    J. Math. Phys. 48(11) (2007) 112901 (30 pp).
    ( https://dx.doi.org/10.1063/1.2801875 ).
    arXiv:0506005 [math-ph].
    Math. Rev. A.M.S. 2009e:70053. Zbl. Math. Zbl 1152.81420.

  38. J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Geometric Hamilton-Jacobi theory''.
    Int. J. Geom. Meth. Mod. Phys. 3(7) (2006) 1417-1458.
    ( https://dx.doi.org/10.1142/S0219887806001764 ).
    arXiv:0604063 [math-ph].
    Math. Rev. A.M.S. 2007m:70040. Zbl. Math. Zbl 1158.70007.

  39. A.M. Rey, N. Román-Roy, M. Salgado.
    ``Günther's formalism (k-symplectic formalism) in classical field theories: Skinner-Rusk approach and the evolution operator''.
    J. Math. Phys. 46(5) (2005) 052901, 24 pp.
    ( https://dx.doi.org/10.1063/1.1876872 ).
    arXiv:0412004 [math-ph].
    Math. Rev. A.M.S. 2006d:70055. Zbl. Math. Zbl 1110.70025.

  40. M. de León, J. Marín-Solano, J.C. Marrero, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Pre-multisymplectic constraint algorithm for field theories''.
    Int. J. Geom. Meth. Mod. Phys. 2(5) (2005) 839-871.
    ( https://dx.doi.org/10.1142/S0219887805000880 ).
    arXiv:0506005 [math-ph].
    Math. Rev. A.M.S. 2008d:70040. Zbl. Math. Zbl 1156.70317.

  41. A. Echeverría-Enríquez, C. López, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Lagrangian-Hamiltonian unified formalism for field theory''.
    J. Math. Phys. 45(1) (2004) 360-380.
    ( https://dx.doi.org/10.1063/1.1628384 ).
    arXiv:0212002 [math-ph].
    Math. Rev. A.M.S. 2004i:70036. Zbl. Math. Zbl 1070.70015.

  42. X. Gràcia, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``On some aspects of the geometry of differential equations in Physics''.
    Int. J. Geom. Meth. Mod. Phys. 1(3) (2004) 265-284.
    ( https://dx.doi.org/10.1142/S0219887804000150 ).
    arXiv:0402030 [math-ph].
    Math. Rev. A.M.S. 2005e:34002. Zbl. Math. Zbl 1076.34005.

  43. A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``On the construction of ${\cal K}$-operators in field theories as sections along Legendre maps''.
    Acta Appl. Math. 77(1) (2003) 1-40.
    ( https://dx.doi.org/10.1023/A:1023671402908 ).
    arXiv:0103019 [math-ph].
    Math. Rev. A.M.S. 2004e:70039. Zbl. Math. Zbl 1028.58001.

  44. A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Geometric reduction in optimal control theory with symmetries''.
    Rep. Math. Phys. 52(1) (2003) 89-113.
    ( https://dx.doi.org/10.1016/S0034-4877(03)90006-1 ).
    arXiv:0206036 [math-ph].
    Math. Rev. A.M.S. 2004h:49037. Zbl. Math. Zbl 1051.49011.

  45. M. de León, J. Marín-Solano, J.C. Marrero, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Singular Lagrangian systems on jet bundles''.
    Fortsch. Phys. 50(2) (2002) 105-169.
    ( https://dx.doi.org/10.1002/1521-3978(200203)50:2 ).
    arXiv:0105012 [math-ph].
    Math. Rev. A.M.S. 1 888 080. Zbl. Math. Zbl 1010.37031.

  46. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``M``ultivector Fields and Connections. Applications to Field Theories''.
    Rev. R. Acad. Ciencias Ser. A: Mat. 96(1) (2002) 83-93.
    Math. Rev. A.M.S. 2003g:70033. Zbl. Math. Zbl 1025.53045.

  47. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``A`` Geometrical Analysis of the Field Equations in Field Theories''.
    Int. J. Math. Math. Sciences 29(12) (2002) 687-700.
    arXiv:0105018 [math-ph].
    Math. Rev. A.M.S. 2002m:70042. Zbl. Math. Zbl 1009.53018.

  48. M.C. Muñoz-Lecanda, N. Román-Roy, J. Yániz-Fernández.
    ``Time-dependent Lagrangians invariant by a vector field''.
    Lett. Math. Phys. 57(2) (2001) 107-121.
    ( https://dx.doi.org/10.1023/A:1017963123948 ).
    arXiv:0102010 [math-ph].
    Math. Rev. A.M.S. 2002f:37090. Zbl. Math. Zbl 1007.37026.

  49. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``On the Multimomentum Bundles and the Legendre Maps in Field Theories''.
    Rep. Math. Phys. 45(1) (2000) 85-105.
    ( https://dx.doi.org/10.1016/S0034-4877(00)88873-4 ).
    arXiv: 9904007 [math-ph].
    Math. Rev. A.M.S. 2002a:70031. Zbl. Math. Zbl 0953.70020.

  50. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Geometry of Multisymplectic Hamiltonian First-order Field Theories''.
    J. Math. Phys. 41(11) (2000) 7402-7444.
    ( https://dx.doi.org/10.1063/1.1308075 ).
    arXiv:0004005 [math-ph].
    Math. Rev. A.M.S. 2002f:70052. Zbl. Math. Zbl 1007.70023.

  51. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Reduction of Presymplectic Manifolds with Symmetry''.
    Rev. Math. Phys. 11(10) (1999) 1209-1247.
    ( https://dx.doi.org/10.1142/S0129055X99000386 ).
    arXiv:9911008 [math-ph].
    Math. Rev. A.M.S. 2001b:53106. Zbl. Math. Zbl 0983.53056.

  52. M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Implicit Quasilinear Differential Systems: a Geometrical Approach''.
    Electron. J. Diff. Eqs. 1999(10) (1999) 1-33.
    Math. Rev. A.M.S. 2000k:34002. Zbl. Math. Zbl 0930.34032.

  53. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries''.
    J. Phys. A: Math. Gen. 32(48) (1999) 8461-8484.
    ( https://dx.doi.org/10.1088/0305-4470/32/48/309 ).
    arXiv:9907007 [math-ph].
    Math. Rev. A.M.S. 2001k:70031. Zbl. Math. Zbl 0982.70019.

  54. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Multivector Fields and Connections. Setting Lagrangian Equations for Field Theories''.
    J. Math. Phys. 39(9) (1998) 4578-4603.
    ( https://dx.doi.org/10.1063/1.532525 ).
    arXiv:9707001 [dg-ga].
    Math. Rev. A.M.S. 99i:58059. Zbl. Math. Zbl 927.37054.

  55. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy, C. Victoria-Monge.
    ``Mathematical foundations of geometric quantization''.
    Extracta Mathematicae 13(2) (1998) 135-238.
    arXiv:9904008 [math-ph].
    Math. Rev. A.M.S. 2000a:53152. Zbl. Math. Zbl 0978.53137.

  56. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Geometry of Lagrangian first-order classical field theories''.
    Fortsch. Phys. 44(3) (1996) 235-280.
    ( https://dx.doi.org/10.1002/prop.2190440304 ).
    arXiv: 9505004 [dg-ga].
    Math. Rev. A.M.S. 97e:58060. Zbl. Math. Zbl 0964.58015.

  57. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``N``on-standard connections in classical mechanics''.
    J. Phys. A: Math. Gen. 28(19) (1995) 5553-5567.
    ( https://dx.doi.org/10.1088/0305-4470/28/19/011 ).
    arXiv: 9503001 [dg-ga].
    Math. Rev. A.M.S. 96k:70020. Zbl. Math. Zbl 870.58006.

  58. M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Gauge systems: presymplectic and group action formulations''.
    Int J. Theor. Phys. 32(11) (1993) 2077-2085.
    ( https://dx.doi.org/10.1007/BF00675021 ).
    Math. Rev. A.M.S. 94m:58086. Zbl. Math. Zbl 797.58026.

  59. M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Lagrangian theory for presymplectic systems''.
    Ann. I. H. Poincaré: Phys. Teor. 57(1) (1992) 27-45.
    Math. Rev. A.M.S. 93j:58052. Zbl. Math. Zbl 760.58018.

  60. X. Gràcia, J.M. Pons, N. Román-Roy.
    ``Higher order conditions for singular Lagrangian dynamics''.
    J. Phys. A: Math. Gen. 25(7) (1992) 1989-2004.
    ( https://dx.doi.org/10.1088/0305-4470/25/7/037 ).
    Math. Rev. A.M.S. 93d:58052. Zbl. Math. Zbl 759.70015.

  61. N. Román-Roy.
    ``Symplectic and non-symplectic realizations of groups for singular systems. An example''.
    Int. J. Theor. Phys. 30(1) (1991) 89-95.
    ( https://dx.doi.org/10.1007/BF00670761 ).
    Math. Rev. A.M.S. 92e:58077. Zbl. Math. Zbl 722.58018.

  62. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
    ``Geometrical setting of time-dependent regular systems: Alternative models''.
    Rev. Math. Phys. 3(3) (1991) 301-330.
    ( https://dx.doi.org/10.1142/S0129055X91000114 ).
    Math. Rev. A.M.S. 92g:58034. Zbl. Math. Zbl 749.58020.

  63. X. Gràcia, J.M. Pons, N. Román-Roy.
    ``Higher order Lagrangian systems: geometric structures, dynamics and constraints''.
    J. Math. Phys. 32(10) (1991) 2744-2763.
    ( https://dx.doi.org/10.1063/1.529066 ).
    Math. Rev. A.M.S. 93a:58061. Zbl. Math. Zbl 778.58025.

  64. C. Batlle, N. Román-Roy.
    ``Algoritmos de obtención de las ligaduras Hamiltonianas y Lagrangianas aplicados al modelo D.G.L. ampliado''.
    Anales Física (A): Fenómenos e Interacs. 84(2) (1989) 131-150.

  65. J.F. Cariñena, C López, N. Román-Roy.
    ``Origin of Lagrangian constraints and their relation with the Hamiltonian formalism''.
    J. Math. Phys. 29(5) (1988) 1143-1149.
    ( https://dx.doi.org/10.1063/1.527955 ).
    Math. Rev. A.M.S. 89e:58044. Zbl. Math. Zbl 644.70013.

  66. N. Román-Roy.
    ``Dynamics of constrained systems''.
    Int. J. Theor. Phys. 27(4) (1988) 427-431.
    ( https://dx.doi.org/10.1007/BF00669391 ).
    Math. Rev. A.M.S. 89h:58066. Zbl. Math. Zbl 655.58017.

  67. C. Batlle, J. Gomis, J.M. Pons, N. Román-Roy.
    ``Lagrangian and Hamiltonian constraints for second order singular Lagrangians''.
    J. Phys. (A): Math. Gen. 21(12) (1988) 2693-2703.
    ( https://dx.doi.org/10.1088/0305-4470/21/12/013 ).
    Math. Rev. A.M.S. 89h:58052. Zbl. Math. Zbl 658.70017.

  68. J. Llosa, N. Román-Roy.
    ``Invariant forms and Hamiltonian systems: a geometrical setting''.
    Int. J. Theor. Phys. 27(12) (1988) 1533-1543.
    ( https://dx.doi.org/10.1007/BF00669290 ).
    Math. Rev. A.M.S. 90b:58081. Zbl. Math. Zbl 676.58031.

  69. J. Llosa. N. Román-Roy.
    ``Descripción geométrica del teorema de Lee Hwa Chung y sus aplicaciones a los sistemas dinámicos Hamiltonianos regulares''.
    Anales Física (A): Fenómenos e Interacs. 84(1) (1988) 13-24.

  70. J.F. Cariñena, C López, N. Román-Roy.
    ``Geometric study on the connection of Lagrangian and Hamiltonian constraints''.
    J. Geom. Phys. IV(3) (1987) 315-334.
    ( https://dx.doi.org/10.1016/0393-0440(87)90017-9 ).
    Math. Rev. A.M.S. 89i:58031. Zbl. Math. Zbl 657.58012.

  71. C. Batlle, J. Gomis, J.M. Pons, N. Román-Roy.
    ``Lagrangian and Hamiltonian constraints''.
    Lett. Math. Phys. 13 (1987) 17-23.
    ( https://dx.doi.org/10.1007/BF00570763 ).
    Math. Rev. A.M.S. 88h:58041. Zbl. Math. Zbl 616.58015.

  72. J.F. Cariñena, J. Gomis, L.A. Ibort, N. Román-Roy.
    ``Applications of the canonical transformations theory for presymplectic systems''.
    Nuovo Cim. (B) 98(2) (1987) 172-196.
    ( https://dx.doi.org/10.1007/BF02721479 ).
    Math. Rev. A.M.S. 88m:58049.

  73. C. Batlle, J. Gomis, J.M. Pons, N. Román-Roy.
    ``On the Legendre transformation for singular Lagrangians and related topics''.
    J. Phys. (A): Math. Gen. 20(15) (1987) 5113-5123.
    ( https://dx.doi.org/10.1088/0305-4470/20/15/027 ).
    Math. Rev. A.M.S. 89f:58051. Zbl. Math. Zbl 642.58029.

  74. C. Batlle, J. Gomis, J.M. Pons, N. Román-Roy.
    ``Equivalence between the Lagrangian and Hamiltonian formalisms for constrained systems''.
    J. Math. Phys. 27(12) (1986) 2953-2962.
    ( https://dx.doi.org/10.1063/1.527274 ).
    Math. Rev. A.M.S. 88a:58060. Zbl. Math. Zbl 613.70012.

  75. J.F. Cariñena, J. Gomis, L.A. Ibort, N. Román-Roy.
    ``Canonical transformations theory for presymplectic systems''.
    J. Math. Phys. 26(8) (1985) 1961-1969.
    ( https://dx.doi.org/10.1063/1.526864 ).
    Math. Rev. A.M.S. 86j:58041. Zbl. Math. Zbl 592.58018.

  76. J. Gomis, J. Llosa, N. Román-Roy.
    ``Lee Hwa Chung theorem for presymplectic manifolds. Canonical transformations for constrained systems''.
    J. Math. Phys. 25(5) (1984) 1348-1355.
    ( https://dx.doi.org/10.1063/1.526303 ).
    Math. Rev. A.M.S. 85k:58030. Zbl. Math. Zbl 553.70014.

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Proceedings


  1. J. Gaset, N. Román-Roy
  2. "Multisymplectic formulation of Lagrangian models in gravitation''.
    In Extended Conference Abstracts (ECAs) GEOMVAP.
    Research Perspectives CRM, Barcelona, Spain. (2021).

  3. P.D. Prieto-Martínez, N. Román-Roy
  4. "Skinner-Rusk unified formalism for higher-order systems''.
    In Proceedings of the XX Fall Workshop on Geometry and Physics 216-220.
    (Madrid, Spain, 2011). Edited by M. Barbero-Liñán, F. Barbero, D. Martín de Diego.
    AIP Conference Proceedings 1460 Melville, New York (2012). ISBN: 978-0-7354-1064-0. ISSN: 0094-243X

  5. N. Román-Roy,M. Salgado, S. Vilariño.
  6. "Symmetries, Noether's theorem and reduction in k-cosymplectic field theories''.
    In Proceedings of the XVIII Fall Workshop on Geometry and Physics 173-179.
    (Benasque, Spain, 2009). Edited by M. Asorey, J.F. Cariñena, J. Clemente-Gallardo, E. Martínez
    AIP Conference Proceedings 1260 Melville, New York (2010). ISBN: 978-0-7354-0809-8. ISSN: 0094-243X.

  7. N. Román-Roy,M. Salgado, S. Vilariño.
  8. "Lie-algebroid formulation of k-cosymplectic classical field theories''.
    In Proceedings of the XVII Fall Workshop on Geometry and Physics 176-181.
    (Castro Urdiales, Spain, 2008). Edited by F. Etayo, M. Fioravanti, R. Santamaría
    AIP Conference Proceedings 1130 Melville, New York (2009). ISBN: 978-O-7354-0666-7. ISSN: 0094-243X.

  9. N. Román-Roy,M. Salgado, S. Vilariño.
  10. ``Symmetries in k-symplectic field theories''.
    In Proceedings of the XVI Fall Workshop on Geometry and Physics 197-201.
    (Lisboa, Portugal, 2007). Edited by R. Loja Fernandes, R. Picken.
    AIP Conference Proceedings 1023 Melville, New York (2008). ISBN: 978-Q-7354-0546-2. ISSN: 0094-243X.

  11. M. Barbero, A. Echeverría-Enríquez, D. Martín de Diego, M.C. Muñoz-Lecanda, N. Román-Roy.
  12. ``Skinner-Rusk formalism for Optimal Control''.
    In Proceedings of the XV Fall Workshop on Geometry and Physics 225-230.
    (Santa Cruz de Tenerife, Spain, 2006). Edited by D. Iglesias,J.C. Marrero, F. Martín-Cabrera, E. Padrón, D. Sosa.
    Pub. Real Sociedad Matemática Española 11 Madrid (2008). ISBN: 978-84-935196-1-2.

  13. N. Román-Roy.
  14. ``Some topics concerning the theory of singular dynamical systems''.
    In Proceedings of the International Workshop on Groups, Geometry and Physics, 215-225.
    (Zaragoza, Spain, 2005). Edited by J. Clemente-Gallardo, E. Martínez.
    Monografías Real Acad. Ciencias Exactas, Físicas, Químicas y Naturales. 29 Zaragoza (2006). ISBN: Z.3.250-2006.

  15. J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.C. Muñoz-Lecanda, N. Román-Roy.
  16. ``A new geometrical setting for the Hamilton-Jacobi equation''.
    In Proceedings of the XIV Fall Workshop on Geometry and Physics, 198-204.
    (Bilbao, Spain, 2005). Edited by L.C. de Andrés, J.J. Arroyo, M. Fernández, O.J. Garay, J.J. Mencía, J. Santisteban.
    Pub. Real Sociedad Matemática Española 8, Madrid (2006). ISBN: 84-933610-7-2.

  17. A. Echeverría-Enríquez, M. de León, M.C. Muñoz-Lecanda, N. Román-Roy.
  18. ``Extended Hamiltonian formalism of field theories: Variational aspects and other topics''.
    In Proceedings of the 7th International Conference on Geometry, Integrability and Quantization, 116-127
    .
     (Varna, Bulgaria, 2005). Edited by I.M. Mladenov, M. de León.
    SOFTEX, Sofia (2006). ISBN: 954-8495-30-9.

  19. M. de León, J. Marín-Solano, J.C. Marrero, M.C. Muñoz-Lecanda, N. Román-Roy.
  20. ``Constraint algorithm for singular field theories''.
    In Proceedings of the XIII Fall Workshop on Geometry and Physics, 233-239.
    (Murcia, Spain, 2004). Edited by J. Alías, A. Ferrández, M.A. Hernández, P. Lucas, J.A. Pastor.
    Pub. Real Sociedad Matemática Española 9, Madrid (2005). ISBN: 84-933610-6-2.

  21. A. Echeverría-Enríquez, C. López, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy.
  22. ``Skinner-Rusk formulation in classical field theory''.
    In Proceedings of the XII Fall Workshop on Geometry and Physics, 211-216.
    (Coimbra, Portugal, 2003). Edited by H. Albuquerque, R.C. Caseiro, J. Clemente-Gallardo, J. Nunes da Costa, J.Teels.
    Pub. Real Sociedad Matemática Española 7, Madrid (2004). ISBN: 84-933610-3-8.

  23. A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy.
  24. ``Symmetries and reduction in optimal control theory''.
    In Proceedings of the XI Fall Workshop on Geometry and Physics, 203-208.
    (Oviedo, Spain, 2002). Edited by J. Fernández-Núñez, W. García Fuentes, A. Viña Escalar.
    Pub. Real Sociedad Matemática Española 6, Madrid (2004). ISBN: 84-933610-1-1.

  25. M.C. Muñoz-Lecanda, N. Román-Roy, F.J. Yániz.
  26. ``Time-dependent Lagrangians invariant by a connection''.
    In Proceedings of the X Fall Workshop on Geometry and Physics, 215-223.
    (Miraflores de la Sierra, Spain, 2001). Edited by A. González-López, et al.
    Pub. Real Sociedad Matemática Española 4 , Madrid (2003). ISBN: 84-923818-8-4.

  27. A. Echeverría-Enríquez, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy.
  28. ``On a kind of field operators for field theories''.
    In Proceedings of the X Fall Workshop on Geometry and Physics, 105-115.
    (Miraflores de la Sierra, Spain, 2001). Edited by A. González-López  et al.
    Pub. Real Sociedad Matemática Española 4 , Madrid (2003). ISBN: 84-923818-8-4.

  29. X. Grácia, M.C. Muñoz-Lecanda, N. Román-Roy.
  30. ``Geometric structures and differential equations''.
    Proceedings of the XVIII CEDYA: Congress on Differential Equations and Applications,
    (Tarragona, Spain, 2003). Edited by J.M. Jornet, J.M. López, C. Olivé, R. Ramírez
    Sociedad Española de Matemática Aplicada (SEMA), Madrid (2003). ISBN 84-930923-2-0.

  31. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
  32. ``Equations and Symmetries in Covariant Hamiltonian Field Theories''.
    In Proceedings of the VIII Fall Workshop on Differential Geometry and Applications, 55-66.
    (Medina del Campo, Spain, 1999). Edited by M.A. del Olmo, M. Santander.
    Pub. Real Sociedad Matemática Española 2, Madrid (2001). ISBN: 84-923818-4-1.

  33. X. Gràcia, M.C. Muñoz-Lecanda, N. Román-Roy.
  34. ``Singular systems: their origins, general features, and non numerical solution'',
    In System Structure and Control 1995.  Proceedings of the IFAC Conference. 37-42.
    (Nantes, France, 1995). Edited by M. Guglielmi, Laboratoire d'Automatique de Nantes.
    Elsevier (1996)  ISBN: 0-08-042356-6.

  35. A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy.
  36. ``Non-standard connections for non-autonomous systems''.
    In Proceedings of the III Fall Workshop on Differential Geometry and Applications, 59-71.
    (Granada, Spain, 1994). Edited by C. Ruiz, A. Romero, M. Sánchez, M.A. Cañadas-Pinedo.
    CIEMAT-Real Sociedad Española de Física.Madrid (1995). ISBN 84-7834-268-0.

  37. C. Batlle, J. Gomis, J.M. Pons, N. Román-Roy.
  38. ``Equivalencia entre los formalismos Lagrangiano y Hamiltoniano con ligaduras''.
    Actas de los Encuentros Relativistas Españoles 85, 150-161.
    (Menorca, Spain, 1985). Ed. Grup de Relativitat, Sec. Física, Inst. Estudis catalans.

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Preprints

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Books


PUBLISHED:

  • M.C. Muñoz-Lecanda, N. Román-Roy.
    Origen y Desarrollo Histórico del Cálculo Infinitesimal  (PDF )
    Ediciones UPC, Barcelona 1999. ISBN 84-8301-360-6.

CHAPTERS:

  1. N. Román-Roy.
  2. "Some properties of multisymplectic manifolds''.
    Classical and Quantum Physics. 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control. 325-336 (2019).
    Edited by G. Marmo, D. Martín de Diego, M.C. Muñoz-Lecanda.
    Springer Proceedings in Physics 229. Springer.
    ( https://doi.org/10.1007/978-3-030-24748-5 18 ).
    arXiv:1807.11774 [math-ph].


  3. J.F. Cariñena, X. Gràcia, G. Marmo, E. Martínez, M.C. Muñoz-Lecanda, N. Román-Roy.
  4. "Hamilton-Jacobi theory and the evolution operator''.
    Mathematical Physics and Field Theory. Julio Abad in memoriam.177-186 (2009).
    Edited by M. Asorey, J.V. García-Esteve, M.F. Rañada, J. Sesma.
    Prensas Univ. Zaragoza. ISBN: 978-84-92774-04-3.
    arXiv:0907.1039v1 [math-ph].

EDITED:

  1. X. Gràcia, J. Marín-Solano, M.C. Muñoz-Lecanda, N. Román-Roy (editors)
  2. Proceedings of the IX Fall Workshop on Geometry and Physics.
    Pub. Real Sociedad Matemática Española III, RSME, Madrid (2001).
    ISBN 84-923818-5-X.
    (Available from the editors).

  3. X. Gràcia, M.C. Muñoz, N. Román-Roy (editors)
  4. Proceedings of the II Fall Workshop on Differential Geometry and its Applications, Barcelona '93
    published in Barcelona by the editors, 1994.
    ISBN 84-605-1284-3.
    (Available from the editors).

  5. A. Berciano, C. Jalón, J. Ling, M. Macho, I. Marrero, M.C. Muñoz, E. Padrón, N. Román Roy, M. Sánchez, M.T. Valdecantos, M.E. Vázquez (editores).
  6. Mujeres y Matemáticas: 13 retratos.
    Comisión Mujeres y Matemáticas, RSME. Bongo Studio. Madrid, 2008.
    ISBN 10 84-935196-2-9, 13 978-84-935196-2-9.
    (Available from the editors).

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Teaching publications and development


TEACHING PUBLICATIONS:

  1. N. Román-Roy.
      Relatividad General: Complementos Matemáticos, Formulación Minkowskiana de la RE, Fundamentos y Ecuaciones de la RG. (PDF )
  2. (2021).
  3. N. Román-Roy.
      Teoría de la Gravitación Newtoniana. Electromagnetismo (PDF )
  4. (2021).
  5. N. Román-Roy.
      Cálculo Diferencial e Integral en Rn (PDF )
  6. (2020).
  7. N. Román-Roy.
      Modelos Matemáticos de la Física: Mecánica Clásica, Electromagnetismo y Relatividad. (PDF )
  8. (2015).
  9. I. Gracia, N. Román-Roy, N. Urbizu.
    Apuntes de Análisis Vectorial  (PDF )
  10. (2007).
  11. I. Gracia, N. Román-Roy.
    Apuntes de Ecuaciones Diferenciales  (PDF )
  12. (2010).
  13. M.C. Muñoz-Lecanda, N. Román-Roy
    Geometría de los Sistemas Dinámicos (PDF)
  14. (2010).

TEACHING DEVELOPMENT:

  1. M. Macho, I. Marrero, E. Padrón, N. Román-Roy, M. Sánchez, E. Vázquez.
  2. ``Situación actual de las mujeres matemáticas españolas en el ámbito de la docencia e investigación universitaria''.
    In Actas del VI Congreso Iberoamericano de Ciencia, Tecnología y Género: "Estudios Iberoamericanos de Género en Ciencia, Tecnología y Salud", 165-170.
    (Zaragoza, Spain, 2006). Edited by C. Miqueo, M.J. Barral, C. Magallón.
    GENCIBER, Prensas Universitarias de Zaragoza. Zaragoza (2008). ISBN: 978-84-7733-971-7.

  3. M. Macho, I. Marrero, E. Padrón, N. Román-Roy, M. Sánchez, E. Vázquez.
  4. ``Algunas conclusiones del primer Encuentro Mujeres y Matemáticas de la Real Sociedad Matemática Española''.
    In Actas del VI Congreso Iberoamericano de Ciencia, Tecnología y Género: "Estudios Iberoamericanos de Género en Ciencia, Tecnología y Salud", 605-609.
    (Zaragoza, Spain, 2006). Edited by C. Miqueo, M.J. Barral, C. Magallón.
    GENCIBER, Prensas Universitarias de Zaragoza. Zaragoza (2008). ISBN: 978-84-7733-971-7.

  5. M. Blanco, R. Eixarch, R. Estela, J. Franch, M. Ginovart, E. Jarauta, N. Román-Roy, S. Xambó.
  6. "Teaching and Learning Calculus using WIRIS Technology in Moodle environment".
    In Proceedings of the International Congress of Mathematicians II, Invited Lectures. 604.
    Madrid (2006). EMS, (2006).

  7. M. Blanco, R. Estela, J. Franch, M. Ginovart, E. Jarauta, N. Román-Roy, S. Xambó.
  8. "Curs de càlcul: una nova metodologia per a la impartició i gestió basades en l'entorn Moodle".
    In Llibre de resums de les comunicacions acceptades. IV Congrés Internacional Docència Universitària i Innovació, 228.
    CIDUI, (2006).

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Scientific Essays


  1. N. Román-Roy.
  2. "Ciencia y tecnología en la obra de Julio Verne'',
    MATEMATICALIA: Revista digital de divulgación matemática 1(4) (2005).

  3. N. Román-Roy.
  4. "Sobre las interacciones fundamentales, las partículas elementales y las teorías de campos'',
    BURAN (Rama Estudiantes del IEEE) 9(1) (1999) 41-44. (PDF )

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