MURAI Hiroko
| Faculty Division of Natural Sciences Research Group of Mathematics | Professor |
Last Updated :2025/06/13
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Profile Information
Name (Japanese)
MuraiName (Kana)
Hiroko
Research History
Education
Professional Memberships
■Ⅱ．研究活動実績
Published Papers
- Refereed, JP Journal of Geometry and Topology, Pushpa Publishing House, FOLDING MOTION IN THAT SHRINKS A GOOD POLYGONAL ANNULUS TO ARBITRARY SMALL NEIGHBORHOOD OF THE INNER BOUNDARY, Hiroko Murai, In 2004, Demaine et al. showed that if is a simply connected polygonal region in the plane, then for any piecewise- folded state of , there exists a folding motion from to [1]. We have shown that if is not simply connected, then the conclusion of the theorem does not necessarily hold, in fact, there exists an annulus in such that there exists a piecewise- folded state of which does not admit folding motions from by using "knot and link theory". From the viewpoint of knot and link theory, it is reasonable to expect that the folded state admits a folding motion from if and only if forms a trivial link in (Conjecture). Note that the 'only if part of the Conjecture is obvious. In this paper, we give a proof of the following statement that will be used in an expected proof of the 'if part of the Conjecture for special kind of annulus.Ifis an annulus such that each of the boundary components bounds a polygonal convex region, then for any , there exists a flat folded state such that is contained in the -neighborhood of the inner boundary of in , denoted by with a strongly flat folding motion from to which satisfies the following:(1) For any , the number of 1 -simplices of the 1 -complex is finite, where denotes the canonical crease pattern of .(2) For any is a good polygonal annulus.(3) For any with , we have ., 24 Dec. 2024, 32, 2, 143, 154, Scientific journal, 10.17654/0972415x24010
- Not Refereed, Dec. 2019, Scientific journal
- Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 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, Oct. 2018, 27, 12, Scientific journal, 10.1142/S0218216518500669
- Refereed, Kobe Journal of Mathematics, Gap of codimension one foliations, MURAI Hiroko, 2012, 29, 1, 24, Scientific journal
- Kyoto-Math Preprint Series, Gap of Depths of Leaves on Codimension One Foliations, Hiroko MURAI, May 2007, 7
- Refereed, JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, Depths of the foliations on 3-manifolds each of which admits exactly one depth 0 leaf, Hiroko Murai, May 2007, 16, 5, 641, 669, Scientific journal, 10.1142/S0218216507005427
- 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
- Not Refereed, Sep. 2022
Presentations
- 07 Mar. 2025, 05 Mar. 2025 - 07 Mar. 2025
- 14 Dec. 2024, 13 Dec. 2024 - 14 Dec. 2024
- 14 Sep. 2024, 14 Sep. 2024 - 16 Sep. 2024
- Hiroko Murai, 8th International Meeting on Origami in Science, Mathematics and Education, Melbourne, 2024., Some applications of topology on origami, Oral presentation, 16 Jul. 2024, 15 Jul. 2024 - 18 Jul. 2024
- Some mathematical treatments of flat foldable and/or rigid foldable origami, Public discourse, 15 Feb. 2024, 15 Feb. 2024 - 15 Feb. 2024
- Invited oral presentation, 16 Dec. 2023, 15 Dec. 2023 - 16 Dec. 2023
- Hiroko Murai; Akari Iwamura, 10th International Congress on Industrial and Applied Mathematics, A remark on the foldability of non-simply connected paper, Oral presentation, 23 Aug. 2023, 20 Aug. 2023 - 25 Aug. 2023
- Hiroko Murai; Reika Yamamoto, On the existence of cylinder solutions of waterbomb tessellation, Oral presentation, 08 Sep. 2022, 08 Sep. 2022 - 10 Sep. 2022
- Oral presentation, 20 Dec. 2019, 18 Dec. 2019 - 21 Dec. 2019
- 2017
- Complexes induced from spherical curves and distances derived from them, 2017
- 2015
- Low dimensional topology and number theory VII, A construction of flat foldable origami via similarity structure, 2015
- 2011
- 2011
- 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
- 2010
- E-KOOK Seminar 2010, 3-manifolds : Proposal for fundamental settings and applications, 2010
- Oral presentation, 09 Nov. 2020 - 11 Nov. 2020
Research Projects
- 基盤研究(C), 01 Apr. 2023 - 31 Mar. 2027, 23K03231, 位相幾何学による折り紙理論の新しい展開とその応用, 村井 紘子, 日本学術振興会, 科学研究費助成事業, 奈良女子大学, 2600000, 2000000, 600000, kaken
- 基盤研究(C), 01 Apr. 2022 - 31 Mar. 2026, 22K03313, 大域構造の空間を基軸とする低次元トポロジーの研究とその応用, 小林 毅; 村井 紘子; 張 娟姫, 日本学術振興会, 科学研究費助成事業, 奈良女子大学, 3250000, 2500000, 750000, kaken
- Grant-in-Aid for Scientific Research (C), 01 Apr. 2013 - 31 Mar. 2017, 25400091, Research on 3-manifold using geometric techniques and its development, Kobayashi Tsuyoshi; BAKER Kenneth; FUNAKOSHI Yukari; HASHIZUME Megumi; IDO Ayako; ICHIHARA Kazuhiro; ITO Noboru; JANG Yeonhee; MURAI Hiroko; OZAWA Makoto; TAKAO Kazuto; RIECK Yo'av, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nara Women's University, 3900000, 3000000, 900000, In this research, we show that, for each n >1, there exist a Heegaard splitting with distance n, and there exists a bridge splitting with distance n. We introduce a new concept on Heegaard theory, called keen Heegaard splitting, and develop the techniques to show that there are keen Heegaard splittings with distance n. Then we show that there are knots each of which admits infinitely many irreducible bridge spheres with arbitrarily high bridge index. We apply the idea of similarity structure on 2-dimensional torus to construct flat foldable origami. Further we show that there are flat foldable origamis that are not constructed by using similarity structure. In addition to these, we define a distance on the set of isotopy classes of the spherical curves, and give some results on it., kaken
- Grant-in-Aid for Young Scientists (B), 2009 - 2012, 21740055, Foliations on three dimensional manifolds, MURAI Hiroko, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nara Women's University, 0, 0, 0, We studied intersections of essential laminations and Heegaard surfaces which give strongly irreducible Heegaard splittings in three dimensional manifolds. It is known that such Heegaard surfaces intersect essential surfaces in essential simple closed curves. We gave a similar result when Heegaard genus is two. We also gave some examples which give a phenomenon specific to non-compact objects., Competitive research funding, kaken
