1990 Fiscal Year Annual Research Report

離散幾何とその応用

Research Project

Project/Area Number	02640066
Research Institution	University 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)
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。

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).
[Publications] H.MAEHARA: "A rigid unitーbar framework without triangle" Matematica Japonica.
[Publications] H.MAEHARA: "Reflecting a triangle in the plane"
[Publications] H.MAEHARA: "A remark on a certain completion of a convex set" Mathematica Japonica. 36. 47-49 (1991)
[Publications] H.MAEHARA: "On the intersection graph of random sets" Discrete Mathematics. 87. 97-104 (1991)
[Publications] H.MAEHARA: "Dispersed points and geometric embedding of complete bipartite graphs" Discrete & Computational Geometry. 6. 57-67 (1991)
[Publications] H.MAEHARA: "Another "MatchーStick" Geometry" Ryukyu Mathematical Journal. 3. 25-37 (1990)
[Publications] H.MAEHARA: "On the dimension to represent a graph by a unit distance graph" Graphs and Combinatorics. 6. 365-367 (1990)
[Publications] T.NISHISHIRAHO: "Direct theorems for best approximation in Banach Spaces" Approximation,Optimization and Computing. 1. 155-158 (1990)
[Publications] T.NISHISHIRAHO: "Saturation of iterations of mutiplier operators in Banach spaces" Ryukyu Mathematical Journal. 3. 45-84 (1990)
[Publications] T.NISHISHIRAHO: "Convergence of guasiーpositive operators" Atti Sem.Mat.Fis.
[Publications] M.FURUSHIMA: "Complex analytic compactifications of C^3" Compositio Mathematica. 76. 163-196 (1990)
[Publications] M.FURUSHIMA: "MukaiーUmemura's example of the Fano threefold with genus 12 as a compactification of C^3" Nagoya Mathematical Journal.
[Publications] M.FURUSHIMA: "Nonーnormal hyperplane section of Fano threefolds of first kind with index two" Ryukyu Mathematical Journal. 3. 1-6 (1990)
[Publications] M.KATO: "On extremal points of a real algebraic function" Mathematica Japonica. 35. 57-64 (1990)
[Publications] K.KODAKA: "Approximately inner ^*ーderivations of irrationa rotation C^*ーalgebras" Tokyo Journal of Mathematics. 13. 207-219 (1990)
[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)
[Publications] K.KODAKA: "Diffeomorphisms of irrational rotation C^*ーalgebras by nonーgeneric rotations II" Journal of Operator Theory.

1990 Fiscal Year Annual Research Report

離散幾何とその応用

Principal Investigator

前原濶琉球大学, 教育学部, 教授 (60044921)

Research Products

[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).

[Publications] H.MAEHARA: "A rigid unitーbar framework without triangle" Matematica Japonica.

[Publications] H.MAEHARA: "Reflecting a triangle in the plane"

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

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

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

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

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

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

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

[Publications] T.NISHISHIRAHO: "Convergence of guasiーpositive operators" Atti Sem.Mat.Fis.

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

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

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

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

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

[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)

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

1990 Fiscal Year Annual Research Report

離散幾何とその応用

Principal Investigator

前原 濶 琉球大学, 教育学部, 教授 (60044921)

Research Products

[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).

[Publications] H.MAEHARA: "A rigid unitーbar framework without triangle" Matematica Japonica.

[Publications] H.MAEHARA: "Reflecting a triangle in the plane"

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

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

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

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

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

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

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

[Publications] T.NISHISHIRAHO: "Convergence of guasiーpositive operators" Atti Sem.Mat.Fis.

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

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

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

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

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

[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)

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

前原濶琉球大学, 教育学部, 教授 (60044921)

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

[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)