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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 3, Pages 21–28 (Mi timm403)  

This article is cited in 6 scientific papers (total in 7 papers)

Object visibility for an observer with inaccurately given coordinates

V. I. Berdyshev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A characteristic is introduced for the visibility of a moving object in the case when the coordinates of the observer are known with an error. The directional differentiability of this characteristic is proved, a differentiation formula is found in the form of an extremal problem, and a refinement theorem is established for this problem.

Keywords: navigation, visibility characteristic, differentiability, refinement.

Full text: PDF file (153 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 268, suppl. 1, S15–S22

Bibliographic databases:

UDC: 519.62
Received: 23.03.2009

Citation: V. I. Berdyshev, “Object visibility for an observer with inaccurately given coordinates”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 3, 2009, 21–28; Proc. Steklov Inst. Math. (Suppl.), 268, suppl. 1 (2010), S15–S22

Citation in format AMSBIB
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\paper Object visibility for an observer with inaccurately given coordinates
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\pages 21--28
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages S15--S22
\crossref{https://doi.org/10.1134/S0081543810050020}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Berdyshev, “Object visibility for a group of observers with inaccurately given coordinates”, Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S40–S47  mathnet  crossref  elib
    2. V. I. Berdyshev, “Moving object and observer in a Banach space”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S68–S73  mathnet  crossref  isi  elib
    3. Berdyshev V.I., “A moving object and an observer in a Banach space”, Dokl. Math., 82:3 (2010), 986–987  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. V. I. Berdyshev, “Object and observer: A surveillance problem”, Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S35–S47  mathnet  crossref  isi  elib
    5. Berdyshev V.I., “Tracking problem: Differentiation of the visibility function”, Doklady Mathematics, 85:1 (2012), 153–155  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. V. I. Berdyshev, “Kharakteristiki skrytosti dvizhuschegosya ob'ekta”, Tr. IMM UrO RAN, 18, no. 4, 2012, 110–119  mathnet  elib
    7. “Vitalii Ivanovich Berdyshev (on his 75th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 1–4  mathnet  crossref  mathscinet
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