Tokushima University / Educator and Researcher Directory --- Ishihara, Toru

○	Mathematics

○	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．)

Academic Paper (Judged Full Paper):

1.	Toru Ishihara : Enumeration of hypergraphs, European Journal of Combinatorics, Vol.22, 503-509, 2001. (Keyword) hypergraph / enumeration
2.	Toru Ishihara : Cameron's construction of two-graphs, Discrete Mathematics, Vol.215, No.1-3, 283-291, 2000. (Link to Publication Site) ● Publication site (DOI): 10.1016/S0012-365X(99)00320-9 (Link to Search Site for Scientific Articles) ● Search Scopus @ Elsevier (DOI): 10.1016/S0012-365X(99)00320-9 (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. (Keyword) harmonic map
4.	Toru Ishihara : Complete nonorientable minimal surfaces in R3, Transactions of American mathematical society, Vol.333, 889-901, 1992. (Keyword) minimal surface / nonorientable surface
5.	Toru Ishihara : Complete Mobious Strips minimally immersed in R3, Proceedings of the American Mathematical Society, Vol.107, 803-806, 1989. (Keyword) minimal surface
6.	Jiro Hamada and Toru Ishihara : Complexity of goodness of dot patterns varying in symmetry, Psychological Research, Vol.50, No.1, 155-161, 1988. (Summary) 実験Ⅰでは3×3行列と4×4行列中に配置されたドット·パターンに対する良さ評定，実験Ⅱでは亀甲模様の枠組中に配置されたドット·パターンに対する良さと複雑さの評定を行なった．実験Ⅰの結果は従来の良さ判断の理論(R&Rサブセット，変換構造説)では説明できない事実を示した．そこで，実験Ⅰと実験Ⅱの結果を総合して，パターンの良さと複雑さが対称変換群の位数の関数で表現できることを示した．
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. (Keyword) harmonic morphism / harmonic map
16.	Toru Ishihara and Goldberg Samuel : Riemanian submersion comuting with Laplacian, Journal of Differential Geometry, Vol.13, No.1, 139-144, 1978. (Keyword) submersion / Laplacian
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. (Keyword) harmonic map / holomorphic map
18.	Toru Ishihara and Goldberg Samuel : Harmonic quasiconformal mappings of Riemannian manifolds, American Journal of Mathematics, Vol.98, No.1, 225-240, 1976. (Keyword) harmonic mapping
19.	Toru Ishihara and Goldberg Samuel : Mappings of bounded dilatation of Riemannian manifolds, Journal of Differential Geometry, Vol.10, No.3, 619-630, 1975. (Keyword) harmonic mapping
20.	Toru Ishihara and Goldberg Samuel : Generalization of Shwarz-Alfors lemma to quasiconformal mappings, Proceedings of synmosia in pure mathematics, Vol.27, 25, 1975. (Keyword) harmonic map
21.	Toru Ishihara and Goldberg Samuel : Harmonic quasiconformal mappings of Riemannian manifolds, Bullein of American mathematical society, Vol.80, 562-566, 1974. (Keyword) harmonic map

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) ● Metadata: 49026 (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) ● Metadata: 111838 (Link to Search Site for Scientific Articles) ● CiNii @ National Institute of Informatics (CRID): 1571698601789951104 (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) ● Metadata: 145 (Tokushima University Institutional Repository: 145)
4.	Toru Ishihara : Decompsitions of Boolean functions and hypergraphs, Journal of Mathematics, Tokushima University, Vol.28, 1-13, 1999. (Keyword) hypergraph / boolean function (Tokushima University Institutional Repository) ● Metadata: 128 (Tokushima University Institutional Repository: 128)
5.	Toru Ishihara : Harmonic maps of noborientable surfaces into complex grassmann manifolds, Journal of Mathematics, Tokushima University, 1994. (Keyword) harmonic mapping (Tokushima University Institutional Repository) ● Metadata: 106 (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. (Keyword) immersion (Tokushima University Institutional Repository) ● Metadata: 96 (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. (Summary) 対称変換群(二面体群と巡回群)を生成する亀甲パターンを新たに考案して，パターンの複雑さと良さに関する評定実験を行なった．実験結果は今井の変換構造説では説明できない事実を示した．群論を導入して，パターンの複雑さは巡回群と二面体群の区別なしにパターンの生成する対称変換群の位数の単調減少関数として，一方パターンの良さは巡回群および二面体群の位数の単調増加関数として表現されることを発見した．
8.	Toru Ishihara : A remark on harmonic quasiconformal mappings, Journal of Mathematics, Tokushima University, Vol.5, No.0, 17-23, 1972. (Summary) K-quasiconformal mappings of Riemann surfaces was investigated by P.J. Kiernan in [2]. One of his interesting results is that harmonic K-quasiconformal mappings of certain Riemann surfaces are distance-decreasing. We shall discuss here harmonic K-quasiconformal mappings of n-dimensional Riemannian manifolds and generalize the above Kiernan's theorem to this case. In section 1 we review the theory of harmonic forms as found in [4]. Section 2 is devoted to get some lemmas which are used to prove our theorem in the last section. Concerning quasiconformal mappings, we use the fact given by H. Wu in [5]. (Keyword) harmonic mapping (Tokushima University Institutional Repository) ● Metadata: 23 (Link to Search Site for Scientific Articles) ● CiNii @ National Institute of Informatics (CRID): 1050564287416010880 (Tokushima University Institutional Repository: 23, CiNii: 1050564287416010880)
9.	Toru Ishihara : On tensor-product structures and grassmannian structures, Journal of Mathematics, Tokushima University, Vol.4, 1-17, 1971. (Keyword) G-structure (Tokushima University Institutional Repository) ● Metadata: 17 (Tokushima University Institutional Repository: 17)
10.	Toru Ishihara : On almost projective structure, Journal of Mathematics, Tokushima University, Vol.3, 37-56, 1970. (Keyword) G-structure / projective structure (Tokushima University Institutional Repository) ● Metadata: 15 (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. (Keyword) two-graph
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.

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)

Professor Emeritus : Ishihara, Toru

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