호남수학학술지 (Honam Mathematical Journal)

  • 제43권4호
  • /
  • Pages.679-689
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  • 2021
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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𝜖-PERTURBATION METHOD FOR VOLUME OF HYPERCUBES CLIPPED BY TWO OR THREE HYPERPLANES

  • Cho, Eungchun (Department of Mathematics, Seoul National University) ;
  • Cho, Yunhi (Department of Mathematics, University of Seoul)
  • 투고 : 2021.06.23
  • 심사 : 2021.09.28
  • 발행 : 2021.12.25
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초록

The first author suggested an exact volume formula of the hypercubes [0, 1]n clipped by several hyperplanes expressed directly in terms of linear coefficients of the hyperplanes. However, it requires awkward assumptions to apply the formula to various situations. We suggest a concrete method to overcome those restrictions for two or three hyperplanes using 𝜖-perturbation, which gives an exact value applicable for any kind of arrangement of hyperplanes with no consideration.

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과제정보

The first author's work at Seoul National University was supported by The Korea Research Foundation and The Korean Federation of Science and Technology Societies Grant funded by Korea Government (MOEHRD,Basic Research Promotion Fund). The second author's work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(No. 2021R1F1A1047226).

참고문헌

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