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Rolling Simplexes and Their Commensurability. II (A Lemma on the Directrix and Focus)

Abstract

The law of central-square dynamics

$$ \left(x,y,z\right)^{{\prime\prime} }=\frac{4{\uppi}^2k}{{\left(\alpha \left(x-a\right)+\beta \left(y-b\right)+\gamma \left(z-c\right)+\delta \right)}^2}\left(x-a,y-b,z-c\right), $$

expressing the focusing of a plane wave at the point (a, b, c) is discussed and justified.

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References

  1. 1.

    O. V. Gerasimova, “Rolling simplexes and their commensurability. I. The axiom and criterion of incompressibility and the momentum lemma,” Fundam. Prikl. Mat., 17, No. 2, 87–95 (2011/2012).

  2. 2.

    Yu. P. Razmyslov, “An explanation to “Rolling simplexes and their commensurability” (field equations in accordance with Tycho Brahe),” Fundam. Prikl. Mat., 17, No. 4, 193–215 (2011/2012).

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Correspondence to O. V. Gerasimova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 1, pp. 13–19, 2014.

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Gerasimova, O.V. Rolling Simplexes and Their Commensurability. II (A Lemma on the Directrix and Focus). J Math Sci 211, 304–309 (2015). https://doi.org/10.1007/s10958-015-2606-z

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Keywords

  • Cauchy Problem
  • Plane Wave
  • Scalar Product
  • Harmonic Oscillator
  • Incompressibility