Researchers Database

MURAI Hiroko

FacultyFaculty Division of Natural Sciences Research Group of Mathematics
PositionAssociate Professor
Last Updated :2022/10/06

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Profile and Settings

  • Name (Japanese)

    Murai
  • Name (Kana)

    Hiroko

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

Association Memberships

  • 日本数学会
  • Mathematical Society of Japan
  • 日本折紙学会, Apr. 2021, 9999

Ⅱ.研究活動実績

Published Papers

  • Refereed, 研究集会「結び目の数理II」報告集, 曲面上のグラフのKrushkal 多項式, 村井紘子; 山村瑠納, Dec. 2019, Scientific journal
  • Refereed, JP Journal of Geometry and Topology, Pushpa Publishing House, SIMILARITY STRUCTURE ON 2-DIMENSIONAL TORUS AND FLAT ORIGAMI, Miki Irii; Tsuyoshi Kobayashi; Hiroko Murai, 31 Jan. 2019, 22, 1, 45, 63, Scientific journal
  • Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, WORLD SCIENTIFIC PUBL CO PTE LTD, 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'])., Oct. 2018, 27, 12, Scientific journal
  • Refereed, Kobe Journal of Mathematics, Gap of codimension one foliations, MURAI Hiroko, 2012, 29, 1, 24, Scientific journal
  • Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, WORLD SCIENTIFIC PUBL CO PTE LTD, 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., May 2007, 16, 5, 641, 669, Scientific journal
  • Refereed, Proceedings of Intelligence of Low Dimensional Topology 2006, Series on Knots and Everything, Gap of the depths of leaves of foliations, MURAI Hiroko, 2007, 40, 223, 230, Scientific journal

Presentations

  • Oral presentation, 09 Nov. 2020, 11 Nov. 2020
  • 研究集会「結び目の数学X」, Complexes induced from spherical curves and distances derived from them, 2017
  • Complexes induced from spherical curves and distances derived from them, 2017
  • Low dimensional topology and number theory VII, A construction of flat foldable origami via similarity structure, 2015
  • Low dimensional topology and number theory VII, A construction of flat foldable origami via similarity structure, 2015
  • The Seventh East Asian School of Knots and Related Topics, Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications, 2011
  • Workshop on topology and geometry - Heegaard splitting of 3-manifolds -, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
  • Workshop on low dimensional topology in Shanghai and Suzhou, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
  • The Seventh East Asian School of Knots and Related Topics, Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications, 2011
  • Workshop on topology and geometry - Heegaard splitting of 3-manifolds -, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
  • Workshop on low dimensional topology in Shanghai and Suzhou, A Haken type theorem on intersections of essential laminations and genus 2 Heegaard surfaces, 2011
  • E-KOOK Seminar 2010, Toward Haken type theorems for essential laminations in 3-manifolds : Proposal for fundamental settings and applications, 2010
  • E-KOOK Seminar 2010, 3-manifolds : Proposal for fundamental settings and applications, 2010
  • 村井紘子; 山村瑠納, 結び目の数理II, 曲面上のグラフのKrushkal多項式について, 20 Dec. 2019, 18 Dec. 2019, 21 Dec. 2019

Research Projects

  • 2009, 2012, 3次元多様体上の葉層構造, 0, 0, 0, Competitive research funding
  • 2009, 2012, Foliations on three dimensional manifolds, 0, 0, 0, Competitive research funding


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