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離散幾何とその応用

Research Project

Project/Area Number 02640066
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionUniversity of the Ryukyus

Principal Investigator

前原 濶  琉球大学, 教育学部, 教授 (60044921)

Co-Investigator(Kenkyū-buntansha) 小高 一則  琉球大学, 理学部, 助手 (30221964)
加藤 満生  琉球大学, 教育学部, 助教授 (50045043)
古島 幹雄  琉球大学, 教育学部, 助教授 (00165482)
中里 治男  琉球大学, 教育学部, 教授 (60044997)
西白保 敏彦  琉球大学, 理学部, 教授 (70044956)
Project Period (FY) 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1990: ¥2,100,000 (Direct Cost: ¥2,100,000)
Keywords単体の折返し / 等辺フレ-ムワ-ク / 剛性 / 代数的数
Research Abstract

離散幾何およびその応用に関して以下の研究結果を得た。
1.R^n内のn次元単体Tに対して、Tの1つの面の決定する超平面に関してTと対称な単体をとることを‘Tを面に関して折り返す'と言う。ある単体Tから出発して、‘面に関して折り返す'操作を次々行って得られる単体達の頂点の集合をΩ(T)で表す。このとき(1)n>2でTがn次元の正則単体ならΩ(T)はR^nで到るところ稠密である。(2)平面上の三角形Tについては、3つの角が(60°,60°,60°),(30°,30°,120°),(45°,45°,90°)(30°,60°,90°)となる4つの場合を除いてΩ(T)は平面上到るところ稠密である。(平面の場合については、P.フランクル(仏)、I.バラニ-(ハンガリ-)の協力による。)
2.n次元ユ-クリッド空間内の辺長1の等辺フレ-ムワ-クに関して、(1)どんな等辺フレ-ムワ-クFもrigidな等辺フレ-ムワ-クに拡大できる。(2)Fがその形を変えずにrigidな等辺フレ-ムワ-クに拡張できるための必要十分条件は、Fの頂点間の距離がすべて代数的数であることである。(3)任意の代数的数r>0はR^n内のrigidな等辺フレ-ムワ-クの2頂点間の距離として実現される。
3.平面上の等辺フレ-ムワ-クでrigidでしかも三角形を持たないものが存在するかという問題に対して、2部グラフとなる平面上のrigidな等辺フレ-ムワ-クを構成してみせた。
そのほか、研究課題と周辺領域に入る多くの結果を得たが、それらについては割愛する。

Report

(1 results)
  • 1990 Annual Research Report
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] H.MAEHARA: "Extending a flexible unitーbar framework to a rigid one" Annals of Discrete Mathematics (to appear in the volume dedicated to the memory of Zdenek Frolic).

    • Related Report
      1990 Annual Research Report
  • [Publications] H.MAEHARA: "A rigid unitーbar framework without triangle" Matematica Japonica.

    • Related Report
      1990 Annual Research Report
  • [Publications] H.MAEHARA: "Reflecting a triangle in the plane"

    • Related Report
      1990 Annual Research Report
  • [Publications] H.MAEHARA: "A remark on a certain completion of a convex set" Mathematica Japonica. 36. 47-49 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] H.MAEHARA: "On the intersection graph of random sets" Discrete Mathematics. 87. 97-104 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] H.MAEHARA: "Dispersed points and geometric embedding of complete bipartite graphs" Discrete & Computational Geometry. 6. 57-67 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] H.MAEHARA: "Another "MatchーStick" Geometry" Ryukyu Mathematical Journal. 3. 25-37 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] H.MAEHARA: "On the dimension to represent a graph by a unit distance graph" Graphs and Combinatorics. 6. 365-367 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.NISHISHIRAHO: "Direct theorems for best approximation in Banach Spaces" Approximation,Optimization and Computing. 1. 155-158 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.NISHISHIRAHO: "Saturation of iterations of mutiplier operators in Banach spaces" Ryukyu Mathematical Journal. 3. 45-84 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] T.NISHISHIRAHO: "Convergence of guasiーpositive operators" Atti Sem.Mat.Fis.

    • Related Report
      1990 Annual Research Report
  • [Publications] M.FURUSHIMA: "Complex analytic compactifications of C^3" Compositio Mathematica. 76. 163-196 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.FURUSHIMA: "MukaiーUmemura's example of the Fano threefold with genus 12 as a compactification of C^3" Nagoya Mathematical Journal.

    • Related Report
      1990 Annual Research Report
  • [Publications] M.FURUSHIMA: "Nonーnormal hyperplane section of Fano threefolds of first kind with index two" Ryukyu Mathematical Journal. 3. 1-6 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] M.KATO: "On extremal points of a real algebraic function" Mathematica Japonica. 35. 57-64 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] K.KODAKA: "Approximately inner ^*ーderivations of irrationa rotation C^*ーalgebras" Tokyo Journal of Mathematics. 13. 207-219 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] K.KODAKA: "Automorphisms of tensor products of irrational rotation C^*ーalgebras and the C^*ーalgebra of compact operators" Tokyo Journal of Mathematics. 13. 457-468 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] K.KODAKA: "Diffeomorphisms of irrational rotation C^*ーalgebras by nonーgeneric rotations II" Journal of Operator Theory.

    • Related Report
      1990 Annual Research Report

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Published: 1990-04-01   Modified: 2016-04-21  

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