Abstract:
Let S be a nondegenerate simplex in Rn and let v be a nonzero n-dimensional vector. We give the computational formulas for the length and endpoints of the longest segment in S parallel to v.
Citation:
M. V. Nevskii, “Computation of the longest segment of a given direction in a simplex”, Fundam. Prikl. Mat., 18:2 (2013), 147–152; J. Math. Sci., 203:6 (2014), 851–854
\Bibitem{Nev13}
\by M.~V.~Nevskii
\paper Computation of the longest segment of a~given direction in a~simplex
\jour Fundam. Prikl. Mat.
\yr 2013
\vol 18
\issue 2
\pages 147--152
\mathnet{http://mi.mathnet.ru/fpm1505}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3431791}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 203
\issue 6
\pages 851--854
\crossref{https://doi.org/10.1007/s10958-014-2175-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84922076775}
Linking options:
https://www.mathnet.ru/eng/fpm1505
https://www.mathnet.ru/eng/fpm/v18/i2/p147
This publication is cited in the following 8 articles:
M. V. Nevskii, “On Properties of a Regular Simplex Inscribed into a Ball”, Aut. Control Comp. Sci., 56:7 (2022), 778
M. V. Nevskii, “O svoistvakh pravilnogo simpleksa, vpisannogo v shar”, Model. i analiz inform. sistem, 28:2 (2021), 186–197
M. Nevskii, A. Ukhalov, “Perfect simplices in $\mathbb{R}^5$”, Beitr. Algebr. Geom., 59:3 (2018), 501–521
M. V. Nevskii, A. Yu. Ukhalov, “Novye otsenki chislovykh velichin, svyazannykh s simpleksom”, Model. i analiz inform. sistem, 24:1 (2017), 94–110
M. V. Nevskii, A. Yu. Ukhalov, “On $n$-dimensional simplices satisfying inclusions $S\subset [0,1]^n\subset nS$”, Automatic Control and Computer Sciences, 52:7 (2018), 667–679
M. V. Nevskii, A. Yu. Ukhalov, “On numerical characteristics of a simplex and their estimates”, Autom. Control Comp. Sci., 51:7 (2017), 757–769
M. V. Nevskii, A. Yu. Ukhalov, “New estimates of numerical values related to a simplex”, Autom. Control Comp. Sci., 51:7 (2017), 770–782
M. V. Nevskii, A. Yu. Ukhalov, “O chislovykh kharakteristikakh simpleksa i ikh otsenkakh”, Model. i analiz inform. sistem, 23:5 (2016), 603–619
Citation in format AMSBIB
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