Coordinate transforms in kinematic changeable sets

1Grushka, Ya.I
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2015, 3:24-31
https://doi.org/10.15407/dopovidi2015.03.024
Section: Mathematics
Language: Ukrainian
Abstract: 

This work is devoted to the study of kinematic changeable sets ("abstract kinematics") that are equipped by different geometrical or topological structures, namely, by metric, topological, linear, Banach, Hilbert, and other spaces. Investigations in this direction may be interesting for astrophysics, because there exists the hypothesis that, on large scales of the Universe, the physical laws (in particular, the laws of kinematics) can be different from the laws acting in the neighborhood of our solar system.

Keywords: coordinate transforms, kinematic changeable sets
References: 

1. Baccetti V., Tate K., Visser M. J. High Energy Phys., 2012, 5: 119. https://doi.org/10.1007/JHEP05(2012)119
2. Hill J. M., Cox B. J. Proc. Roy. Soc., 2012, 468, No 2148: 4174–4192. https://doi.org/10.1098/rspa.2012.0340
3. Vieira R. S. An introduction to the theory of tachyons, http://arxiv.org/pdf/1112.4187.pdf.
4. Recami E. Riv. Nuovo Cim., 1986, 9, S. 3, No 6: 1–178.
5. Grushka Ya. I. Methods of Functional Analysis and Topology, 2013, 19, No 2: 127–145.
6. Grushka Ya. I. Zb. pr. In-tu matematyky NAN Ukrainy, 2013, 10, No 2: 138–169 (in Ukrainian).
7. Grushka Ya. I. Abstract concept of changeable set, http://arxiv.org/pdf/1207.3751.pdf.
8. Grushka Ya. I. Pr. In-tu matematyky NAN Ukrainy, 2014. 11, No 1: 192–227 (in Ukrainian).