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Variation of Singular spaces

Research Project

Project/Area Number 09640086
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionFUKUSHIMA UNIVERSITY

Principal Investigator

MATSUI Akinori  Education, Fukushima Univ., Professor, 教育学部, 教授 (70106102)

Co-Investigator(Kenkyū-buntansha) MAKINO Ryouhei  Education, Fukushima Univ., Professor, 教育学部, 教授 (60106953)
ISHII Hiroyuki  Education, Fukushima Univ., Professor, 教育学部, 教授 (90007360)
ISU Minoru  Education, Fukushima Univ., Professor, 教育学部, 教授 (20007347)
OHASHI Katsuhiro  Economic, Fukushima Univ., Professor, 経済学部, 教授 (40007430)
Project Period (FY) 1997 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Keywordsgraph / Jacobi field / Hamilton graph / eigenvalue / Walsh series / 特異空間 / 特性類 / 張力ベクトル
Research Abstract

First Matsui studied the variation of a graph embedded in a Riemannian manifold. Let each edge of a graph have the property of springs on tension. Suppose that a graph is embedded in a Riemannian manifold such that each edge is geodesical. On this situation, we will introduce the notion of a tension vector at each vertex of a graph and that of a tension Jacobi field on a graph. If an expanded graph moves in the Euclidian space by the influence of tension, then it moves to such direction that the sum of the sizes of its tension vectors. Then we propose the following.
The sum of the sizes of tension vectors decreases if the graph moves along to the tension Jacobi field. If the ambient Riemannian manifold has negative curvature, this claim is true, but this claim is not always true. We construct examples which are not satisfied with this claim.
Next Matsui studied the generalization of the notion of Hamiltonian graphs. Ishii studied the eigenvalue problem for the system of second order linear differential equations. Ohashi studied the functional central limit theorem for Walsh series with general gaps.

Report

(4 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report

Research Products

(4 results)

All Other

All Publications (4 results)

  • [Publications] Hiroyuki ISHII: "A generalization of eigenvalue probles for system of second order linear differential equations"Science reports of Fukushima Univ.. 63. 1-11 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Katuhiro OHASHI: "On the functional central limit theorem for Walsh series with general gaps"Shogaku Ronshu. 67. 81-90 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 石井博行: "A generalization of eigenvalue problems for system of second order linear differential equations"福島大理科報告. 63. 1-11 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 大橋 勝弘: "On the Functional Central Limit Theorem for walsh series with general gaps" The Shogaku Roushu. 67. 81-90 (1999)

    • Related Report
      1998 Annual Research Report

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Published: 1998-03-31   Modified: 2016-04-21  

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