Discrete Quantum Transitions, Duality: Emergence of Physical Structures and Occurrence of Observed Formations (Hidden Properties of Mathematical Physics Equations)

Show more

References

[1] Cartan, E. (1945) Les Systemes Differentiels Exterieurs et Leurs Applications Geometriques. Hermann & Cie, Paris.

[2] Petrova, L.I. (2020) Skew-Symmetric Differential Forms. Conservation Laws. The Foundation of Equations of Mathematical Physics and Equations of Field Theory. KRASAND, Moscow.

[3] Petrova, L.I. (2010) Role of Skew-Symmetric Differential Forms in Mathematics.

http://arxiv.org/pdf/1007.4757.pdf

[4] Bott, R. and Tu, L.W. (1982) Differential Forms in Algebraic Topology. Springer, New York.

https://doi.org/10.1007/978-1-4757-3951-0

[5] Smirnov, V.I. (1957) A Course of Higher Mathematics. Vol. 4, Tech. Theor. Lit., Moscow. (In Russian)

[6] Petrova, L.I. (2009) Relationships between Discontinuities of Derivatives on Characteristics and Trajectories. Computational Mathematics and Modeling, 20, 367-372.

https://doi.org/10.1007/s10598-009-9043-0

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

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

[9] Petrova, L.I. (2012) Physical Meaning and a Duality of Concepts of Wave Function, Action Functional, Entropy, the Pointing Vector, the Einstein Tensor. Journal of Mathematics Research, 4, 78-88.

https://doi.org/10.5539/jmr.v4n3p78

[10] Petrova, L. (2018) Connection between Functions of the Field-Theory Equations and State Functionals of the Mathematical Physics Equations. Journal of Physics: Conference Series, 1051, Article No. 012025.

https://doi.org/10.1088/1742-6596/1051/1/012025

[11] Petrova, L.I. (2017) Features of Numerical Simulation of Euler and Navier-Stokes Equations. Computational Mathematics and Modeling, 28, 32-36.

https://doi.org/10.1007/s10598-016-9343-0

[12] Petrova, L.I. (2003) Exterior and Evolutionary Skew-Symmetric Differential Forms and Their Role in Mathematical Physics.

http://arxiv.org/pdf/math-ph/0310050v1.pdf

[13] Tonnelat, M.A. (1959) Les principles de la Theorie Electromagnetique et la Relativite. Masson, Paris.

[14] Petrova, L. (2013) Role of the Conservation Laws in Evolutionary Processes and Generation of Physical Structures. American Journal of Modern Physics, 2, 104-110.

https://doi.org/10.11648/j.ajmp.20130203.12

[15] Petrova, L.I. (2020) Formatting Physical Fields and Pseudometric Manifolds. The Dark Matter. Journal of Physics: Conference Series, 1557, Article No. 012032.

https://doi.org/10.1088/1742-6596/1557/1/012032

[16] Petrova, L.I. (2012) Integrability and the Properties of Solutions to Euler and Navier-Stokes Equations. Journal of Mathematics Research, 4, 19-28.

https://doi.org/10.5539/jmr.v4n3p19