1. JGD
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  3. 1(8), 2009
  4. Mathematical model of generalized geometry of physical space in geophysical problems

Mathematical model of generalized geometry of physical space in geophysical problems

JGD.
2009;
Volume 8, Number 1
: 97-106
https://doi.org/10.23939/jgd2009.01.097
Authors:
  1. V.M. Karpenko
  2. Yu. P. Starodub
1
SE "Naukanaftogaz" NJSC "Naftogaz Ukrainy"
2
Lviv State University of Life Safety; Scientific-Research Institute "Naukanaftogaz", Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine)

In the article, conclusion and research of the primary mathematical object of the generalized geometry, named – equation of the Gaussian line are considered. Equation unites the mathematical objects of differential, integral and Euclid geometries. Research of this equation by the numerical methods of small finite elements is examined. The equation’s properties reveal the quality change of the line at consideration of differentinitial conditions, time and space step of discretization. It is set that taking into account the theory of power metamorphism, the generalized law of energy conservation, change, transfer and energy pack, equation of the line model the stochastic motion.

equation of generalized geometry
law of energy conservation
law of energy transfer.
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