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Research

Field of Study

○ Mathematics

Subject of Study

○ graph theory (graph, hypergraph, two-graph, signed graph) (符号付きグラフの局所スイッチイングについて調べている．符号付伏見グラフなどの局所スイッチイングによる変形，符号付グラフに含まれる符号付サイクルの挙動などを調べることで，符号付きグラフの構造の解明を行いたい．)

Book / Paper

Academic Paper (Judged Full Paper):

1. Toru Ishihara :
Enumeration of hypergraphs,
European Journal of Combinatorics, Vol.22, 503-509, 2001.
2. Toru Ishihara :
Cameron's construction of two-graphs,
Discrete Mathematics, Vol.215, No.1-3, 283-291, 2000.
(DOI: 10.1016/S0012-365X(99)00320-9)
3. Toru Ishihara :
Harmonic maps of nonorientable surfaces into four-dimensional manifolds,
Tohoku Mathematical Journal, Vol.45, No.1, 1-12, 1993.
4. Toru Ishihara :
Complete nonorientable minimal surfaces in R3,
Transactions of American mathematical society, Vol.333, 889-901, 1992.
5. Toru Ishihara :
Complete Mobious Strips minimally immersed in R3,
Proceedings of the American Mathematical Society, Vol.107, 803-806, 1989.
6. Jiro Hamada and Toru Ishihara :
Complexity of goodness of dot patterns varying in symmetry,
Psychological Research, Vol.50, No.1, 155-161, 1988.
7. Toru Ishihara :
Maximal spacelike submanifolds of pseudo-Riemannian space of constant curvature,
Michigan Journal of Mathematics, Vol.35, No.2, 345-352, 1988.
8. Toru Ishihara :
The Euler characteristics and Weyl's curvature invariants of submaniholds in spheres,
Journal of Mathematical Society of Japan, Vol.39, No.2, 1987.
9. Toru Ishihara :
Kinematic formulas for Weyl's curvature invariants of submanifolds in complex projective space,
Proceedings of the American Mathematical Society, Vol.97, 483-487, 1986.
10. Toru Ishihara :
Total curvature of Kaheler manifolds in complex projective spaces,
Geometiae Dedicate, Vol.20, No.2, 307-318, 1986.
11. Toru Ishihara :
The Gauss map and nonholomorphic harmonic maps,
Proceedings of the American Mathematical Society, Vol.89, 661-665, 1983.
12. Toru Ishihara :
Total curvature of manifolds in self-immersed manifolds,
Manuscripta Mathematica, Vol.39, No.1, 210-218, 1982.
13. Toru Ishihara :
Harmonic Gauss map in a generalaized sence,
Journal of Londan matehmatical Society, Vol.(2)26, No.1, 104-112, 1981.
14. Toru Ishihara :
Radii of immeresed manifolds and nonexistence of immersions,
Proceedings of the American Mathematical Society, Vol.78, No.2, 276-279, 1980.
15. Toru Ishihara :
A mapping of Riemannian manifolds which preserves harmonic functions,
Journal of Mathematics of Kyoto University, Vol.19, No.1, 215-229, 1979.
16. Toru Ishihara and Goldberg Samuel :
Riemanian submersion comuting with Laplacian,
Journal of Differential Geometry, Vol.13, No.1, 139-144, 1978.
17. Toru Ishihara :
The index of a holomorphic mappings of Riemannian manifolds,
Proceedings of the American Mathematical Society, Vol.66, No.1, 169-174, 1977.
18. Toru Ishihara and Goldberg Samuel :
Harmonic quasiconformal mappings of Riemannian manifolds,
American Journal of Mathematics, Vol.98, No.1, 225-240, 1976.
19. Toru Ishihara and Goldberg Samuel :
Mappings of bounded dilatation of Riemannian manifolds,
Journal of Differential Geometry, Vol.10, No.3, 619-630, 1975.
20. Toru Ishihara and Goldberg Samuel :
Generalization of Shwarz-Alfors lemma to quasiconformal mappings,
Proceedings of synmosia in pure mathematics, Vol.27, 25, 1975.
21. Toru Ishihara and Goldberg Samuel :
Harmonic quasiconformal mappings of Riemannian manifolds,
Bullein of American mathematical society, Vol.80, 562-566, 1974.

Academic Paper (Unrefereed Paper):

1. Toru Ishihara :
Local switching of signed induced cycles,
Journal of Mathematics, The University of Tokushima, Vol.39, 1-7, 2005.
(Tokushima University Institutional Repository: 49026)
2. Toru Ishihara :
Local Switching of Some Signed Graphs,
Journal of Mathematics, The University of Tokushima, Vol.38, No.0, 1--7, 2004.
(Tokushima University Institutional Repository: 111838,   CiNii: 1571698601789951104)
3. Toru Ishihara :
Signed graphs associated with the latticed An,
Journal of Mathematics, The University of Tokushima, Vol.36, 1-6, 2003.
(Tokushima University Institutional Repository: 145)
4. Toru Ishihara :
Decompsitions of Boolean functions and hypergraphs,
Journal of Mathematics, Tokushima University, Vol.28, 1-13, 1999.
(Tokushima University Institutional Repository: 128)
5. Toru Ishihara :
Harmonic maps of noborientable surfaces into complex grassmann manifolds,
Journal of Mathematics, Tokushima University, 1994.
(Tokushima University Institutional Repository: 106)
6. Toru Ishihara :
Nonexistence of projective plane immersed with some embeddiness,
Journal of Mathematics, Tokushima University, Vol.26, 9-17, 1992.
(Tokushima University Institutional Repository: 96)
7. Jiro Hamada and Toru Ishihara :
亀甲模様の構造と複雑さおよび良さ判断,
徳島大学総合科学部創立記念論文集, 117-122, 1987.
8. Toru Ishihara :
A remark on harmonic quasiconformal mappings,
Journal of Mathematics, Tokushima University, Vol.5, No.0, 17-23, 1972.
(Tokushima University Institutional Repository: 23,   CiNii: 1050865122808530176)
9. Toru Ishihara :
On tensor-product structures and grassmannian structures,
Journal of Mathematics, Tokushima University, Vol.4, 1-17, 1971.
(Tokushima University Institutional Repository: 17)
10. Toru Ishihara :
On almost projective structure,
Journal of Mathematics, Tokushima University, Vol.3, 37-56, 1970.
(Tokushima University Institutional Repository: 15)

Proceeding of International Conference:

1. Toru Ishihara :
Harmonic qusiconformal mappings of Riemannian manifolds,
82, Jan. 1976.

Proceeding of Domestic Conference:

1. Toru Ishihara :
局所スイッチング，伏見木， 木,
日本数学会年会, Sep. 2005.
2. Toru Ishihara :
符号付伏見木の局所シィッチング,
日本数学会年会, Sep. 2004.
3. Toru Ishihara :
C-tree と Two-graph の対応,
日本数学会年会, Mar. 2004.
4. Toru Ishihara :
正論理関数とハイパーグラフ,
日本数学会年会, Apr. 1997.
5. Toru Ishihara :
ハイパーグラフの数え上げ,
日本数学会年会, Apr. 1997.
6. Toru Ishihara :
向きつけ不可能な極小局面について,
89年度微分幾何学シンポジューム, Aug. 1989.
7. Toru Ishihara :
絶対曲率に関するChern-Lashofの定理について,
83年度微分幾何学会シンポジュウム, Aug. 1983.
8. Toru Ishihara :
Harmonic K-quasiconformal mapping and Schwarz Lemma,
73, Jul. 1973.

Grants-in-Aid for Scientific Research (KAKEN Grants Database @ NII.ac.jp)

  • 多様体上の幾何構造および力学的構造の研究 (Project/Area Number: 07640120 )
  • 多様体上の幾何構造と関連する調和写像の研究 (Project/Area Number: 06640148 )
  • 漸近的方法による非線形備微分方程式の研究 (Project/Area Number: 04640235 )
  • 向き付け不可能な曲面の極小挿入と調和写像の研究 (Project/Area Number: 03640069 )
  • フラクタル自己相似図形の解析的研究 (Project/Area Number: 02640131 )
  • 代数系の等式と変換システムの組合せ論的研究 (Project/Area Number: 01540055 )
  • 擬リーマン多様体の部分多様体と調和写像の研究 (Project/Area Number: 63540052 )
  • ソリトン理論にあらわれる微分方程式の研究 (Project/Area Number: 62540119 )
  • Search by Researcher Number (80035328)