M. V. Nevskij, “On a Property of $n$-Dimensional Simplices”, Mat. Zametki, 87:4 (2010), 580–593; Math. Notes, 87:4 (2010), 543

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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 580–593
DOI: https://doi.org/10.4213/mzm7698 (Mi mzm7698)

This article is cited in 30 scientific papers (total in 30 papers)

On a Property of

n

$n$ -Dimensional Simplices

M. V. Nevskij

P. G. Demidov Yaroslavl State University

Full-text PDF (496 kB) Citations (30)

References:

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DOI: https://doi.org/10.4213/mzm7698

Abstract: Suppose that

$n\in\mathbb N$ and

$S$ is a simplex in

$\mathbb R^n$ , containing the cube

$[0,1]^n$ . It is proved that, for some

$i=1,\dots,n$ , the simplex

$S$ contains an interval of length

$n$ parallel to the

$i$ th coordinate axis. The relationship with questions arising in linear interpolation of continuous functions of

$n$ variables is noted.

Keywords:

$n$ -dimensional simplex, polytope, barycentric coordinates, axial diameter, interpolation projection operator, Steiner symmetrization, Hadamard number.

Received: 22.04.2009
Revised: 03.07.2009

English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 543–555
DOI: https://doi.org/10.1134/S0001434610030326

Bibliographic databases:

Document Type: Article

UDC: 517.51+514.17

Language: Russian

Citation: M. V. Nevskij, “On a Property of

$n$ -Dimensional Simplices”, Mat. Zametki, 87:4 (2010), 580–593; Math. Notes, 87:4 (2010), 543–555

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm7698

https://doi.org/10.4213/mzm7698

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This publication is cited in the following 30 articles:

M. V. Nevskii, “On the Minimal Norm of the Projection Operator for Linear Interpolation on the $n$-Dimensional Ball”, Math. Notes, 114:3 (2023), 415–418
Nevskii M.V., Ukhalov A.Yu., “Linear Interpolation on a Euclidean Ball in Double-Struck Capital R-N”, Autom. Control Comp. Sci., 54:7 (2020), 601–614
M. V. Nevskii, A. Yu. Ukhalov, “Lineinaya interpolyatsiya na evklidovom share v ${\mathbb R}^n$”, Model. i analiz inform. sistem, 26:2 (2019), 279–296
Nevskii M.V., “On Some Problems For a Simplex and a Ball in R-N”, Autom. Control Comp. Sci., 53:7 (2019), 644–652
Mikhail V. Nevskii, Alexey Yu. Ukhalov, “Linear Interpolation on a Euclidean Ball in Rⁿ”, Model. anal. inf. sist., 26:2 (2019), 279
M. V. Nevskii, A. Yu. Ukhalov, “O minimalnom koeffitsiente pogloscheniya dlya $n$-mernogo simpleksa”, Model. i analiz inform. sistem, 25:1 (2018), 140–150
M. V. Nevskii, A. Yu. Ukhalov, “On optimal interpolation by linear functions on an $n$-dimensional cube”, Automatic Control and Computer Sciences, 52:7 (2018), 828–842
M. V. Nevskii, A. Yu. Ukhalov, “Nekotorye svoistva $0/1$-simpleksov”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 18:3 (2018), 305–315
Nevskii M., Ukhalov A., “Perfect Simplices in R-5”, Beitr. Algebr. Geom., 59:3 (2018), 501–521
M. V. Nevskii, “O nekotorykh zadachakh dlya simpleksa i shara v ${\mathbb R}^n$”, Model. i analiz inform. sistem, 25:6 (2018), 680–691
Nevskii M.V., Ukhalov A.Yu., “On Minimal Absorption Index For An N-Dimensional Simplex”, Autom. Control Comp. Sci., 52:7 (2018), 680–687
Nevskii M.V., Ukhalov A.Yu., “On Optimal Interpolation By Linear Functions on N-Dimensional Cube”, Autom. Control Comp. Sci., 52:7 (2018), 828–842
Mikhail V. Nevskii, “On Some Problems for a Simplex and a Ball in R<sup>n</sup>”, Model. anal. inf. sist., 25:6 (2018), 680
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, “New Estimates of Numerical Values Related to a Simplex”, Aut. Control Comp. Sci., 51:7 (2017), 770
M. V. Nevskii, A. Yu. Ukhalov, “On Numerical Characteristics of a Simplex and Their Estimates”, Aut. Control Comp. Sci., 51:7 (2017), 757
M. V. Nevskii, A. Yu. Ukhalov, “O chislovykh kharakteristikakh simpleksa i ikh otsenkakh”, Model. i analiz inform. sistem, 23:5 (2016), 603–619
M. V. Nevskii, “On Some Results in the Geometry of Convex Bodies and their Applications”, Model. anal. inf. sist., 19:3 (2015), 113
Akopyan A.V., Glazyrin A.A., “On Maximum Volume Simplices in Polytopes”, Period. Math. Hung., 69:2 (2014), 251–256

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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