• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Applied Geometry

Research Project

Project/Area Number 07404002
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

MATUMOTO Takao  Fac.Sci., HIROSHIMA UNIVERSITY Prof., 理学部, 教授 (50025467)

Co-Investigator(Kenkyū-buntansha) NISHIURA Yasumasa  Hokkaido U., RIES,Prof., 電子科学研究所, 教授 (00131277)
MUTA Taizo  Fac.Sci., Prof., 理学部, 教授 (80025353)
FUJIKOSHI Yasunori  Fac.Sci., Prof., 理学部, 教授 (40033849)
HARADA Koichi  Fac.Int.Arts Sci., Prof., 総合科学部, 教授 (90124114)
SAEKI Osamu  Fac.Sci., Assoc.Prof., 理学部, 助教授 (30201510)
今岡 光範  広島大学, 教育学部, 教授 (20031817)
谷崎 俊之  広島大学, 理学部, 教授 (70142916)
田端 正久  広島大学, 理学部, 教授 (30093272)
Project Period (FY) 1995 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥25,600,000 (Direct Cost: ¥25,600,000)
Fiscal Year 1998: ¥5,500,000 (Direct Cost: ¥5,500,000)
Fiscal Year 1997: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1996: ¥5,200,000 (Direct Cost: ¥5,200,000)
Fiscal Year 1995: ¥11,600,000 (Direct Cost: ¥11,600,000)
KeywordsVisible geometry / 3- amd 4-manifolds / Information geomtry / Comutational geometry / Boundary surface / Deformation of surfaces / 2-dimensional knot / 見える 幾何学 / 3次元空間 / 曲線・曲面 / 情報幾何 / 計算幾何 / 力学系 / 4次元空間 / 幾何学センター / 境界面の構造 / 曲線の曲面
Research Abstract

We are seeking how to study the applied geometry, by organizing the applied geometry seminar and symposium "Visible Geometry". The new topics and methods in the study of curves and surfaces in 3-space, the structure of the boundary surface and its move, the structure of 3-dimensional or 4-dimensional manifolds, dynamical approach, algebraic and algorithmic approach to geometry, information geometric aspect are the main contents of our recent study.
Matumoto investigates the deformation of generic surfaces in 3-space by the visible geometric methods with applications to the study of surfaces in 4-space especially of the 2-dimensionza1 knots, besides the study of information and computational geometry. Agaoka classified the tilings of the sphere by the rectangle triangles. Saeki is interested in the global study of the manifolds and mappings from the view point of singularity theory, and found a new topological meaning of curvature and tangential developping surface of the curve in 3-spac … More e. Yoshida found a relation between the boundary and characteristic classes. Nakayama extends the notion of Lyapunov function and studied the space of orbits. Doi handles the counting problem of plane curves. Harada defined the curvature for the discrete data to approximate efficiently by a polygonal curve and proposed a method to remove the unnecessary data. Tabata is working on the finite element analysis with some geometric considerations. Nishiura improves the softwear to pursue the branching solutions and studies the self-replicating dynamics. Irie studies the time evolution of space-structure and strategy for a population dynamics. Muta investigated the quantum theoretic phase structures in the curved spacetime. Tanisaki studied the geometric structure of quantum group by D-module. Imaoka studies some algorithms for the various invariants in topology. In information geometric aspects Matumoto characterized the statistical manifold by two point function and Fujikoshi studies the asymptotic expansions and error estimates in statistics. Less

Report

(5 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • 1995 Annual Research Report
  • Research Products

    (43 results)

All Other

All Publications (43 results)

  • [Publications] 松本堯生: "Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds" Hiroshima Mathematical Journal. 28. 207-212 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 佐伯修: "微分可能写像の大域的特異点理論の現状と展望" 数学. 48. 385-399 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 原田耕一: "Approximation polygonal curves in two and three dimensions" Graphical Models and Image Processing. 60. 222-225 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 藤越康祝: "Sharp error bounds for asymptotic expansion of the distribution functions of stale mixture" Ann.Inst.Statist.Math.49. 285-297 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 今岡光範: "A solution of Sylvester's matrix equation" Int.J.Math.Edu.in Sci.and Tech.27. 471-473 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 牟田泰三: "Dynamical symmetry breaking in curved spacetime" Prog.Theor.Physics Suppl.127. 93-193 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 西浦廉政: "岩波書店" 非線形問題I -パターン形成の数理, 279 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Takao Matumoto: "Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds" Hiroshima Mathematical Journal. 28. 207-212 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Osamu Saeki: "A survey on the global singularity theory of smooth mappings" Sugaku. 48. 385-399 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Koichi Harada: "Approximation polygonal curves in two and three dimensions" Graphical Models and Image Processing. 60. 222-225 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasunori Fujikoshi: "Sharp error bounds for asymptotic expansion of the distribution functions of scale mixture" Annales Inst.Statist.Math.49. 285-297 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Mitsunori Imaoka: "A solution of Sylvester's matrix equation" Intern.J.Math.Edu.in Sci.& Tech.27. 471-473 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Taizo Muta: "Dynamical symmetry breaking in curved spacetime" Prog.Theor, Physics (Suppl.). 127. 93-193 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Yasumasa Nishiura: Non-linear problems I-Mathematics for patern formulations. Iwanami Shoten, 1-279 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 松本 尭生: "Classification of closed oriented 4-manifolds modulo connected sum with simply connected manifolds" Hiroshima Mathematical Journal. 28. 207-212 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 佐伯 修: "微分可能写像の大域的特異点理論の現状と展望" 数学. 48. 385-399 (1996)

    • Related Report
      1998 Annual Research Report
  • [Publications] 原田 耕一: "Approximation polygonal curves in two and three dimensions" Graphical Models and Image Processing. 60. 222-225 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 藤越 康祝: "Sharp error bounds for asymptotic expansion of the distribution functions of scale mixture" Ann.Inst.Statist.Math.49. 285-297 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 今岡 光範: "A solution of Sylvester's matrix equation" Int.J.Math.Edu.in Sci.and Tech.27. 471-473 (1996)

    • Related Report
      1998 Annual Research Report
  • [Publications] 牟田 泰三: "Dynamical symmetry breaking in curved spacetime" Prog.Theor.Physics Suppl.127. 93-193 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 西浦 廉政: "岩波書店" 非線形問題I -パターン形成の数理, 279 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 松本堯生: "A gap theorem for Lusternik-Schnirelman π-category" Topology and its Applications. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 佐伯修: "On topological invariance of weights for quasi-homigeneous polynomials" Pitman Research Notes in Mathematics. 381. 207-214 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 西浦廉政: "Connecting Orbit Structures of Monotone Solutions in the Shadorc Systems" Journal of Differential Equations. 140-2. 309-364 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 原田耕一: "Effective data reduction by the curvature-based polygonal approximation" Transactions of IEICE of Japan. E80-D. 250-258 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 今岡光範: "A solution of Sylvester's matrix equation" Int.J.of Math.Edu.in Sci.and Tech.27. 471-473 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 藤越康祝: "Modified AIC and Cp statistic in regression model" Biometrika. 84. 707-716 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 谷崎俊之: "環と体3" 岩波書店, 147 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 松本尭生: "Lusternik-Schnirelmann category and knot complement II" Topology. 34. 177-184 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] 佐伯 修: "Simple stable maps of 3-manifolds into surfaces" Topology. 35. 671-698 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 田端正久: "Air flow computation around an automated guided vehicle" Int. J. of Computational Fluid Dynamics. 7. 155-162 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 原田耕一: "The cone intersection method for min-# polygonal approximation in R^2" Trans. IEICE of Japan. E79D. 343-348 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 今岡光範: "A solution of Sylvester's matrix equation" Int. J. of Math. Edu. in Sei. and Tech.27. 471-473 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 藤越康祝: "Estimation and model selection in an extended growth curve model" Hiroshima Math. J.26. 635-647 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 谷崎俊之: "D加群と代数群" シュプリンガー・フェルラーク東京, 308 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] 松本 堯生: "Lusternik-Schnirelmann category and knot complement II" Topolocy. 34. 177-184 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 佐伯 修: "Constructing generic smooth maps of a manifold into a surface with prescribed singular loci" Annales de l′Institut Fourier. 45. 1135-1162 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 田端 正久: "Air flow computation around an automated guided vehicle" Int. J. of Computational Fluid Dynamics. (to appear). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 原田 耕一: "The cone intersection method for min-♯ polygonal approximation in R^2" Trans. IEICE of Japan. (to appear)E79D. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 今岡 光範: "A solution of Sylvester′s matrix equation" Int. J. of Math. Edu. in Scu, a Tech.(to appear). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 藤越 康祝: "The effects of nonnormality on tests for dimonsion ality in canonical correlation and MANOVA models" J. Multivariate Analysis. 52. 325-337 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 谷崎俊之: "D加群と代数群" シュプリング-・フェルラーク東京, 308 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 牟田泰三: "電磁力学" 岩波書店, 206 (1993)

    • Related Report
      1995 Annual Research Report

URL: 

Published: 1995-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi