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INVERSE PROBLEMS OF SCATTERING : MATHEMATICS,NUMERICAL ANALYSIS AND GRAPHICS

Research Project

Project/Area Number 07404004
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionOsaka University

Principal Investigator

IKAWA Mitsuru  Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (80028191)

Co-Investigator(Kenkyū-buntansha) MORIOKA Tatsushi  Graduate School of Sciences, Osaka Univ., Assist., 大学院・理学研究科, 助手 (80239631)
ISOZAKI Hiroshi  Graduate School of Sciences, Osaka Univ., Assoc.Prof., 大学院・理学研究科, 助教授 (90111913)
MATSUMURA Akitaka  Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (60115938)
SAKANE Yusuke  Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (00089872)
KOTANI Shin-ichi  Graduate School of Sciences, Osaka Univ., Prof., 大学院・理学研究科, 教授 (10025463)
藤木 明  大阪大学, 理学部, 教授 (80027383)
Project Period (FY) 1994 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥18,800,000 (Direct Cost: ¥18,800,000)
Fiscal Year 1996: ¥5,900,000 (Direct Cost: ¥5,900,000)
Fiscal Year 1995: ¥12,900,000 (Direct Cost: ¥12,900,000)
KeywordsScattering / Inverse problem / Numerical analysis / Greobner basis / Einstein metric / Schrodinger operators / Einstein計算 / グラフィク / 正則化 / 非適切問題 / ランダム媒質
Research Abstract

Concerning the inverse problems for Schrodinger operatores, H.Isozaki studied deeply and got very important results. Starting from the idea of Faddeev, Isozaki made clear the relationship between the potential of Schrodinger operators and the scattering amplitude. This relationship shown by Isozaki gives a representation of the solution of the inverse problem for the Schrodinger operators. He was invited to several international conferences and was given a high evaluation.
Concerning the another core of our research, that is, numerical analysis, we introduced computers of Silicon Graphic Co.Ltd., Chalenge Indigo 2 and Indy. By the leadership of Sakane, with cooperation of graduate students (especially with Senda), we studied algorism for getting Greobner basis. Needless to say, Greobner basis play an essential role in various problems related to polynomial rings. But in order to get Greobner basis explicitely for given concrete problems, it becomes a huge computation and it takes a lot of time. So, it is very important to improve algorithm into a efficient ones.
We succeeded to make a new algorism, named GRASIS,which enable us to acheive computation of Greobner basis much faster than before. As an application of our invention of new algorism GRASIS,we found new Einstein metrics.
We have to confess that the term of our research has ended before we set about numerical analysis of inverse scattering problems. We shall continue the numerical study of inverse problems.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] A. Matsumura: "Uniform boudedness of the solutions for a one-dimensional isentropic model system of compressible viscousgas" Comm. Math.: Physics. 175. 259-274 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y. Komatsu: "A fiburcation phenomenon for the periodic solutions of Duffing equarion" Kyoto J. Math.(掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H. Isozaki: "Multi-dimensional inverse scattering theory for Schrodinger overators" Reviews in Math. Physics. 8. 591-622 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] C. Gerard: "N-body resolvent estimates" J. Math. Sec. Japan. 48. 135-160 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H. Isozaki: "Inversc scatteing theory for Dirac operators" Ann. I'Instilut Herni Poincare. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T. Morioka: "Hypoelliptocite four un certain operateur a carateristique double" Tsubuka J. Matl.(掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 井川 満: "偏微分方程式入門" 裳華房, 319 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 小谷真一: "岩波講座現代数学の基礎「測度と確率1」" 岩波書店, 158 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.Matsumura and S.Yanagi: "Uniform boundedness of the solutions for a one-dimensional isentropic medel system of compressible viscous gas" Comm.Math.Physics. vol.175. 259-274 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Komatsu, T.Kano and A.Matsumura: "A bifurcation phenomenon for the priodic solutions of Duffing equation" Kyoto J.Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Isozaki: "Multi-dimensional inverse scattering theory for Schrodinger operators" Review Math.Physics. vol.8. 591-622 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] C.Gerard, H.Isozaki and E.Skibsted: "N-body resolvent estimates" J.Math.Soc.Japan. vol.48. 135-160 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] H.Isozaki: "Inverse scattering theory for Dirac operators" Ann.Inst.H.Poincare. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Morioka: "Hypoellicpticite pour un certain operateur a caracteristique double" Tsukuba J.Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Ikawa: Introduction to theory of particial differential equations. Shokado, 313 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] S.Kotani: Measure theory and probability 1. Iwanami, 158 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] A.Matsumura: "Uniform boundednces of the solutions for a onedimensional isontropic model system of compreesible viscons gas" Comm.Math.Physics. 175. 259-274 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Komatsu: "A bifurcation phenomenon for the periodic solutions of Duffing equation" Kyoto J.Math.(掲載予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Isozaki: "Multi-dimensional inverse scottering theory for Schrodiuger operators" Reviews in Math.Physics. 8. 591-622 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] C.Gerard: "N-body resolvent estimates" J.Math.Soc.Japan. 48. 135-160 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] H.Isozaki: "Inverse scattering theory for Dirac operators" Ann.l'Institute Henri Poincare. (掲載予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Morioka: "Hypoellipticite four un certain overateur a caracteristique double" Tsukuba J.Math.(掲載予定).

    • Related Report
      1996 Annual Research Report
  • [Publications] 井川 満: "偏微分方程式論入門" 裳 華房, 319 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 小谷真一: "測度と確率1「岩波講座 現代数学の基礎」" 岩波書店, 158 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] A.Matsumura: "Analytic approach to Yor's formula of exponential additive functionals of Brownian motion" 伊藤清先生80才記念論文集. (to appear). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] A.Matsumura: "Nonlinear stability of viscous shockprofile for a non-convex system of risouelasticity" to appear in Comm. Math. Pby.(1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Y.Komatsu: "A bifurcation phenomenon for the periodic solutions of the Duffing equation" to appear in J. Math. Kyoto Univ.(1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] J.S.Park: "Invariant Einstein metrics on certain homogeneous spaces" to appear in Tokyo J. Math.

    • Related Report
      1995 Annual Research Report
  • [Publications] A.Fujiki: "Kahler quofients and eguivariant cohomology" Proc.Sympogium on moceuli of vecfor bundles. 39-53 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 井川 満: "偏微分方程式入門" 裳華房, 330 (1996)

    • Related Report
      1995 Annual Research Report

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

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