Nonidentical relations of skew-symmetric forms: Generation of closed exterior forms. Discrete transitions. Connection between field-theory equations and nonidentical relations

  • Authors

    • Ludmila Petrova Moscow State University Faculty of Computational Mathematics & Cybernetics
    2016-10-08
    https://doi.org/10.14419/ijams.v4i2.6635
  • Degenerate transformation, discrete transitions, nonidentical and identical relations, non-integrable manifolds, skew-symmetric forms.

  • Abstract

    Nonidentical relations of skew-symmetric differential forms, which basis are non-integrable deforming manifolds follow from differential equations. From nonidentical relations closed exterior forms are obtained. The process of obtaining closed exterior forms describes the discrete transitions and the emergence of structures and observable formations such as waves, vertices, and turbulent pulsations. It is shown that the field theory equations (by Schroedinger, Maxwell, Einstein and others) turns to be nonidentical relations, obtained from the mathematical physics equations for material media such as the cosmologic systems, the systems of charged particles and others.   

  • References

    1. [1] Cartan E., Les Systemes Differentials Exterieus ef Leurs Application Geometriques, Hermann, Paris, (1945).

      [2] Petrova L.I., Exterior and evolutionary differential forms in mathematical physics: Theory and Applications, Lulu.com, (2008).

      [3] Petrova L.I., “Role of skew-symmetric differential forms in mathematicsâ€, http://arxiv.org/pdf/1007.4757vl.pdf , (2010).

      [4] Petrova L.I., A new mathematical formalism: Skew-symmetric differential forms in mathematics, mathematical physics and field theory, URSS (Moscow), Moscow, (2013).

      [5] Bott R., Tu L.W., Differential Forms in Algebraic Topology, Springer, NY, (1982).

      [6] Clarke J.F., Machesney M.,The Dynamics of Real Gases, Butterworths, London, (1964).

      [7] Tolman R.C., Relativity, Thermodynamics, and Cosmology, Clarendon Press, Oxford, UK, (1969).

      [8] Pauli W., Theory of Relativity, Pergamon Press, (1958).

      [9] Petrova L., “The Peculiarity of Numerical Solving the Euler and Navier-Stokes Equationsâ€, American Journal of Computational Mathematics, Vol.4, No. 4, (2013), pp.305-310.

      [10] Petrova L.I., Hidden properties of the equations of mathematical physics. Evolutionary relation for the state functionals and its connection with the field-theory equations, Journal of Progressive Research in Mathematics(JPRM), Vol.4, No. 2, 2015, pp. 309-320

      [11] Petrova L.I., Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor, Journal of Mathematics Research, Vol. 4, No. 3, (2012), 78-88.

      [12] Einstein A., The Meaning of Relativity, Princeton, (1953).

      [13] Tonnelat M.-A., Les principles de la theorie electromagnetique et la relativite, Masson, Paris, (1959).

  • Downloads

  • How to Cite

    Petrova, L. (2016). Nonidentical relations of skew-symmetric forms: Generation of closed exterior forms. Discrete transitions. Connection between field-theory equations and nonidentical relations. International Journal of Advanced Mathematical Sciences, 4(2), 30-36. https://doi.org/10.14419/ijams.v4i2.6635