Not Refereed, Sep. 2022
Not 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, 10.17654/gt022010045
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, 10.1142/S0218216518500669
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, 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
Kyoto-Math Preprint Series, Gap of Depths of Leaves on Codimension One Foliations, Hiroko MURAI, May 2007, 7
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, Oral presentation, 20 Dec. 2019, 18 Dec. 2019, 21 Dec. 2019
Hiroko Murai; Reika Yamamoto, 日本応用数理学会2022年度年会, On the existence of cylinder solutions of waterbomb tessellation, Oral presentation, 08 Sep. 2022, 08 Sep. 2022, 10 Sep. 2022
村井紘子, MIMS/CMMA トポロジーとその応用融合研究セミナー, Some mathematical treatments of flat foldable and/or rigid foldable origami, Public discourse, 15 Feb. 2024, 15 Feb. 2024, 15 Feb. 2024
村井紘子, 文科省共同利用・共同研究拠点 MIMS「現象数理学研究拠点」共同研究集会「折り紙の科学を基盤とするアート・数理および工学への応用Ⅳ」, トポロジーと折り紙ー folding motion を許容しない folded state の存在についてー, 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