Criterion for the existence of a universal coordinate transformation in kinematic variable sets

Grushka Yaroslav

Grushka Yaroslav ¹

¹ Department of nonlinear analysis, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, 01001, Ukraine

Keywords: criterion of existence, kinematic variable sets

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Abstract

This work is devoted to the investigation of kinematic changeable sets (“abstract kinematics”), that is the mathematical objects, in which changeable sets are equipped with different geometrical or topological structures, namely metric, topological, linear, Banach, Hilbert and other spaces. In the paper a definition of actual and universal coordinate transforms in kinematic changeable sets is presented, and necessary and sufficient condition for the existence of universal coordinate transform is obtained. Investigations in this direction may be interesting for astrophysics, because there exists the hypothesis, that in a large scale of the Universe, physical laws (in particular, the laws of kinematics) may be different from the laws, acting in a neighborhood of our solar System.

References

[1] Valentina Baccetti, Kyle Tate, and Matt Visser. Inertial frames without the relativity principle // Preprint: arXiv:1112.1466v3. – 2012.

[2] James M. Hill and Barry J. Cox. Einstein’s special relativity beyond the speed of light. // Proceedings of the Royal Society. – Published on-line, 3 October 2012 in advance of the print journal (doi:10.1098/rspa.2012.0340).

[3] Ricardo S. Vieira. An Introduction to the Theory of Tachyons. – Preprint: arXiv:1112.4187v2. – 2012.

[4] E. Recami. Classical Tachyons and Possible Applications. // Riv. Nuovo Cim. – 9 , s. 3, N 6. – 1986. – pp. 1-178.

[5] Grushka Ya.I. Tachyon Generalization for Lorentz Transforms // Methods of Functional Analysis and Topology. – 20 , N 2. – 2013. – P. 127-145.

[6] Grushka Y.I. Algebraic properties of tachyon Lorentz transformations // Collection of works of the Institute of Mathematics of NASU. - 2013, N 2, p. 138-169.

[7] Grushka Y.I. Variable sets and their properties // Doklady NASU. - 2012, N 5. - P. 12-18.

[8] Ya.I. Grushka. Abstract concept of changeable set // Preprint arXiv:1207.3751v1. – 2012.

[9] Grushka Y.I.. Visibility in changing sets // Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. - 9, N 2. - 2012. - P. 122-145.

[10] Grushka Y.I. Variable sets and their application for the construction of tachyon kinematics // Proceedings of the Institute of Mathematics of NASU. - 11, N 1. - 2014. - P. 192-227.

[11] Grushka Y. I.. Basic variable sets and mathematical modeling of the evolution of systems // Ukr. math. zhurnal - 65, N 9. - 2013. - P. 1190-1210.

[12] G. Birkhoff. Lattice theory. - M.: Nauka, 1984. - 567 p.

[13] Grushka Y. I.. Evolutionary extensions and analogs of the union operation for basic variable sets // Proceedings of the Institute of Mathematics of the National Academy of Sciences of Ukraine. - 11, N 2. - 2014.

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ACS Style: Grushka, Y. Criterion for the existence of a universal coordinate transformation in kinematic variable sets. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Grushka Y. Criterion for the existence of a universal coordinate transformation in kinematic variable sets. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style: Yaroslav Grushka. 2016. "Criterion for the existence of a universal coordinate transformation in kinematic variable sets". Bukovinian Mathematical Journal. 2 no. 2-3.

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