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Generalizations of Casey’s Theorem for Higher Dimensions. / Abrosimov, N. V.; Aseev, V. V.

In: Lobachevskii Journal of Mathematics, Vol. 39, No. 1, 01.01.2018, p. 1-12.

Research output: Contribution to journal › Article › peer-review

Harvard

Abrosimov, NV & Aseev, VV 2018, 'Generalizations of Casey’s Theorem for Higher Dimensions', Lobachevskii Journal of Mathematics, vol. 39, no. 1, pp. 1-12. https://doi.org/10.1134/S199508021801002X

APA

Abrosimov, N. V., & Aseev, V. V. (2018). Generalizations of Casey’s Theorem for Higher Dimensions. Lobachevskii Journal of Mathematics, 39(1), 1-12. https://doi.org/10.1134/S199508021801002X

Vancouver

Abrosimov NV, Aseev VV. Generalizations of Casey’s Theorem for Higher Dimensions. Lobachevskii Journal of Mathematics. 2018 Jan 1;39(1):1-12. doi: 10.1134/S199508021801002X

Author

Abrosimov, N. V. ; Aseev, V. V. / Generalizations of Casey’s Theorem for Higher Dimensions. In: Lobachevskii Journal of Mathematics. 2018 ; Vol. 39, No. 1. pp. 1-12.

BibTeX

@article{78780a27c3b94ae58f4f5301b539a118,
title = "Generalizations of Casey{\textquoteright}s Theorem for Higher Dimensions",
abstract = "We give generalizations of Casey{\textquoteright}s theorem and its converse for higher dimensions. We also present a multidimensional generalization for the problem of Apollonius. To do this we introduce a notion of ψ-tangent for a generalized k-sphere that touches a number of generalized n-balls in proper manner.",
keywords = "Casey{\textquoteright}s theorem, problem of Apollonius, Ptolemy{\textquoteright}s theorem, Casey's theorem, ANALOG, Ptolemy's theorem",
author = "Abrosimov, {N. V.} and Aseev, {V. V.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1134/S199508021801002X",
language = "English",
volume = "39",
pages = "1--12",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "1",

}

RIS

TY - JOUR

T1 - Generalizations of Casey’s Theorem for Higher Dimensions

AU - Abrosimov, N. V.

AU - Aseev, V. V.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We give generalizations of Casey’s theorem and its converse for higher dimensions. We also present a multidimensional generalization for the problem of Apollonius. To do this we introduce a notion of ψ-tangent for a generalized k-sphere that touches a number of generalized n-balls in proper manner.

AB - We give generalizations of Casey’s theorem and its converse for higher dimensions. We also present a multidimensional generalization for the problem of Apollonius. To do this we introduce a notion of ψ-tangent for a generalized k-sphere that touches a number of generalized n-balls in proper manner.

KW - Casey’s theorem

KW - problem of Apollonius

KW - Ptolemy’s theorem

KW - Casey's theorem

KW - ANALOG

KW - Ptolemy's theorem

UR - http://www.scopus.com/inward/record.url?scp=85042129212&partnerID=8YFLogxK

U2 - 10.1134/S199508021801002X

DO - 10.1134/S199508021801002X

M3 - Article

AN - SCOPUS:85042129212

VL - 39

SP - 1

EP - 12

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 1

ER -

ID: 12081466