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Fundamentalnaya i Prikladnaya Matematika, 2006, Volume 12, Issue 1, Pages 57–94 (Mi fpm923)  
This article is cited in 4 scientific papers (total in 4 papers)

Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems

N. S. Gusev

N. E. Bauman Moscow State Technical University
Full-text PDF (386 kB) Citations (4) English version article
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Abstract: In this paper, canonical decompositions of arbitrary piecewise affine mappings are constructed. Then the equivalence of these mappings is introduced and the concept of polyhedron-trace is defined as an equivalence class. Finally, the concepts of the volume and the deformation of polyhedra-traces are introduced, the continuity of the volume is proved, and the formula of first variation is obtained. These concepts give an analog of the Plateau principles.
English version:
Journal of Mathematical Sciences (New York), 2008, Volume 149, Issue 1, Pages 896–921
DOI: https://doi.org/10.1007/s10958-008-0034-z
Bibliographic databases:
UDC: 514.144.23+514.172.45+514.177.2
Language: Russian
Citation: N. S. Gusev, “Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems”, Fundam. Prikl. Mat., 12:1 (2006), 57–94; J. Math. Sci., 149:1 (2008), 896–921
Citation in format AMSBIB
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\by N.~S.~Gusev
\paper Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 1
\pages 57--94
\mathnet{http://mi.mathnet.ru/fpm923}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2249680}
\zmath{https://zbmath.org/?q=an:1156.57018}
\elib{https://elibrary.ru/item.asp?id=9166885}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 1
\pages 896--921
\crossref{https://doi.org/10.1007/s10958-008-0034-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38349188943}
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  • https://www.mathnet.ru/eng/fpm923
  • https://www.mathnet.ru/eng/fpm/v12/i1/p57
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Фундаментальная и прикладная математика
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    References:89
    First page:1
     
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