Abstract
The paper is an addition to the paper of Yu. I. Babenko and V. A. Zalgaller published in the same volume. It gives a condition under which the set of all vertices of several coaxial prisms inscribed in a sphere in \(\mathbb{R}_3\) has power invariants I1,...,In. A finite set in \(\mathbb{R}_3\) with 11 invariants is constructed. It is also proved that unions of prisms yield finite sets in \(\mathbb{R}_3\) with any preassigned number n of invariants with alternating signs. Bibliography: 5 titles.
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REFERENCES
Yu. I. Babenko and V. A. Zalgaller, “Power invariants of certain point sets” Zap. Nauchn. Semin. POMI, 261, 7-30 (1999).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow (1963).
V. V. Makeev, “On sets with prescribed number of power invariants” Zap. Nauchn. Semin. POMI, 261, 40-42 (1999).
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Yu. I. Babenko, Power Relations in a Circumference and a Sphere, Norell Press, Landisville (1998).
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Babenko, U.I. Power Invariants of a Union of Coaxial Prisms. Journal of Mathematical Sciences 110, 2769–2773 (2002). https://doi.org/10.1023/A:1015389910042
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DOI: https://doi.org/10.1023/A:1015389910042