Researchers Database

MURAI Hiroko

    Faculty Division of Natural Sciences Research Group of Mathematics Associate Professor
Contact:
muraicc.nara-wu.ac.jp
Last Updated :2021/06/02

researchmap

Research Interests

  • 平坦折り 折り紙 葉層構造 多様体 結び目 flat folding origami foliation manifold knot 

Research Areas

  • Natural sciences, Geometry

Research Experience

  • 2009 - 2012, :国立大学法人奈良女子大学 理学部
  • 2009 - 2012, :Faculty of Science,Nara Women'sUniversity
  • 2012, -:国立大学法人奈良女子大学 研究院 自然科学系 数学領域
  • 2012, -:Faculty of Science,Nara Women'sUniversity
  • 2008 - 2009, :東京電機大学情報環境学部
  • 2008 - 2009, :Tokyo Denki University School of Information Environment
  • 助教
  • 助教
  • 助教
  • Assistant Professor
  • Assistant Professor
  • Assistant Professor

Education

  • - 2007, Nara Women's University, 人間文化研究科, Japan
  • - 2007, Nara Women's University, Graduate School, Doctral Research Course in Human Culture
  • - 2002, Kyoto University, Faculty of Science, Japan
  • - 2002, Kyoto University, Faculty of Science

Published Papers

  • 曲面上のグラフのKrushkal 多項式

    村井紘子; 山村瑠納

    Dec. 2019, 研究集会「結び目の数理II」報告集

    Scientific journal

  • SIMILARITY STRUCTURE ON 2-DIMENSIONAL TORUS AND FLAT ORIGAMI

    Miki Irii; Tsuyoshi Kobayashi; Hiroko Murai

    Pushpa Publishing House, 31 Jan. 2019, JP Journal of Geometry and Topology, 22 (1), 45 - 63, doi;url

    Scientific journal

  • A distance on the equivalence classes of spherical curves generated by deformations of type RI

    Funakoshi, Yukari; Hashizume, Megumi; Ito, Noboru; Kobayashi, Tsuyoshi; Murai, Hiroko

    In this paper, we introduce a distance (d) over bar (w)(3) on the equivalence classes of spherical curves under deformations of type RI and ambient isotopies. We obtain an inequality that estimate its lower bound (Theorem 1). In Theorem 2, we show that if for a pair of spherical curves P and P', (d) over bar (w)(3)([P],[P']) = 1 and P and P' satisfy a certain technical condition, then P' is obtained from P by a single weak RIII only. In Theorem 3, we show that if P and P' satisfy other conditions, then P' is ambient isotopic to a spherical curve that is obtained from P by a sequence of a particular local deformations, which realizes (d) over bar (w)(3)([P], [P'])., WORLD SCIENTIFIC PUBL CO PTE LTD, Oct. 2018, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 27 (12), doi;web_of_science

    Scientific journal

  • Gap of codimension one foliations

    MURAI Hiroko

    2012, Kobe Journal of Mathematics, 29, 1 - 24

    Scientific journal

  • Depths of the foliations on 3-manifolds each of which admits exactly one depth 0 leaf

    Hiroko Murai

    In [ 2], Cantwell-Conlon introduced a knot invariant, called depth. In this paper, we discuss the depth of a foliation F on a 3- manifold with F being (*) " codimension one, transversely oriented, taut, and proper". We show that for each n > 0, there exists a 3-manifold M such that ( minimal depth of F on M with F being (*) and having exactly one depth 0 leaf) is greater than ( minimal depth of F on M with F being (*)) + n., WORLD SCIENTIFIC PUBL CO PTE LTD, May 2007, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 16 (5), 641 - 669, doi;web_of_science

    Scientific journal

  • Gap of the depths of leaves of foliations

    MURAI Hiroko

    2007, Proceedings of Intelligence of Low Dimensional Topology 2006, Series on Knots and Everything, 40, 223 - 230

    Scientific journal

Presentations

  • Complexes induced from spherical curves and distances derived from them

    研究集会「結び目の数学X」, 2017

  • Complexes induced from spherical curves and distances derived from them

    2017

  • A construction of flat foldable origami via similarity structure

    Low dimensional topology and number theory VII, 2015

  • A construction of flat foldable origami via similarity structure

    Low dimensional topology and number theory VII, 2015

  • Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications

    The Seventh East Asian School of Knots and Related Topics, 2011

  • A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces

    Workshop on topology and geometry - Heegaard splitting of 3-manifolds -, 2011

  • A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces

    Workshop on low dimensional topology in Shanghai and Suzhou, 2011

  • Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications

    The Seventh East Asian School of Knots and Related Topics, 2011

  • A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces

    Workshop on topology and geometry - Heegaard splitting of 3-manifolds -, 2011

  • A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces

    Workshop on low dimensional topology in Shanghai and Suzhou, 2011

  • Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications

    E-KOOK Seminar 2010, 2010

  • 3-manifolds : Proposal for fundamental settings and applications

    E-KOOK Seminar 2010, 2010

Association Memberships

  • 日本数学会

  • Mathematical Society of Japan



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