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Research in inverse problems by methods of microlocal analysis and its application to practice

Research Project

Project/Area Number 26400184
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research Institution防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群)

Principal Investigator

Takiguchi Takashi  防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, 総合教育学群, 准教授 (50523023)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords超局所解析 / 逆問題 / インフラ再整備 / 環境問題 / 非破壊検査
Outline of Final Research Achievements

I studied inverse problems by methods of microlocal analysis from the viewpoint of both theory and application. In this research, in view of mutual return between theory and application, we also tried to promote collaboration among industry, engineering and mathematics. As research tasks, I studied the following problems in relation with microlocal analysis and inverse problems; representation of vortex sheets in fluid, uniqueness in Radon transform which is basic for the theory of CT, mathematical model for motion of aqueous solutions in the soil, mathematical sciences to establish an acoustic CT for concrete structures, mathematical model for concentration of radionuclides which is indispensable for environmental rearrangement in Fukushima area after the disastrous accident of FD1NPP.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (17 results)

All 2017 2016 2015 2014 2012

All Journal Article (3 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results) Presentation (12 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results) Funded Workshop (2 results)

  • [Journal Article] How the computerized tomography was practicalized2015

    • Author(s)
      Takashi Takiguchi
    • Journal Title

      Bulletin of JSSAC

      Volume: 21 Pages: 50-57

    • Related Report
      2014 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Achievements by Professor Akira Kaneko2014

    • Author(s)
      Tsutomu Sakurai and Takashi Takiguchi
    • Journal Title

      Complex Variables and Elliptic Equations

      Volume: 59 Issue: 11 Pages: 1501-1506

    • DOI

      10.1080/17476933.2012.701290

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Unique continuation of microlocally analytic functions and their structure2012

    • Author(s)
      Takashi Takiguchi
    • Journal Title

      Complex Variables and Elliptic Equations

      Volume: (published on-line first) Issue: 11 Pages: 1507-1519

    • DOI

      10.1080/17476933.2012.744402

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] Representation of the vortex sheets in the perfect fluid by hyperfunctions2017

    • Author(s)
      Takashi Takiguchi
    • Organizer
      復旦大学航天系談話会
    • Place of Presentation
      復旦大学
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Practicalization of computerized tomography and a system of linear equations with no solution2016

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Various problems in partial differential equations
    • Place of Presentation
      日本大学
    • Year and Date
      2016-03-03
    • Related Report
      2015 Research-status Report
  • [Presentation] Acoustic CT for Concrete Structures2016

    • Author(s)
      Takashi Takiguchi
    • Organizer
      11th AIMS International Conference
    • Place of Presentation
      Hyatt Regence Orlando
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多孔質媒体中における移流・異常拡散方程式について2015

    • Author(s)
      羽田野祐子 滝口孝志
    • Organizer
      第16回地下環境 回地下環境 回地下環境 水文 学に関する研究集会 学に関する研究集会 学に関する研究集会 学に関する研究集会
    • Place of Presentation
      大同大学
    • Year and Date
      2015-11-22
    • Related Report
      2015 Research-status Report
  • [Presentation] Development of ultrasonic tomography for concrete structures2015

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Mathematical Backgrounds and Future Progress of Practical Inverse Problems
    • Place of Presentation
      九州大学
    • Year and Date
      2015-11-13
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] On mathematical background of practicalization of computerized tomography at its initial stage2015

    • Author(s)
      Takashi Takiguchi
    • Organizer
      解析学の耳袋
    • Place of Presentation
      沼津市
    • Year and Date
      2015-10-30
    • Related Report
      2015 Research-status Report
  • [Presentation] 非線型マッチングによるせん断変形不変な照合に関する一考察2015

    • Author(s)
      長谷川誠,石原聖司,古川貴雄,滝口孝志
    • Organizer
      電子情報通信学会総合大会
    • Place of Presentation
      立命館大学
    • Year and Date
      2015-03-11
    • Related Report
      2014 Research-status Report
  • [Presentation] ラドン変換と非線型マッチングによるアフィン変形不変な文字認識方法の提案2015

    • Author(s)
      長谷川誠,石原聖司,古川貴雄,滝口孝志
    • Organizer
      電子情報通信学会 PRMU
    • Place of Presentation
      東北大学
    • Year and Date
      2015-02-19
    • Related Report
      2014 Research-status Report
  • [Presentation] On the idea for practicalization of the computerized tomography at its initial stage2015

    • Author(s)
      Takashi Takiguchi
    • Organizer
      微分方程式の逆問題とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-01-26
    • Related Report
      2014 Research-status Report
  • [Presentation] On the representation of the vortex sheets in the ideal fluid2015

    • Author(s)
      Takashi Takiguchi
    • Organizer
      若手による流体力学の基礎方程式研究集会
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Year and Date
      2015-01-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On uniqueness problems for the Radon transform2014

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Several aspects of microlocal analysis
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-10-23
    • Related Report
      2014 Research-status Report
  • [Presentation] An inverse problem for the heat equation in view of practical application2014

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Inverse Problems -- from theory to application
    • Place of Presentation
      At-Bristol, Bristol, UK
    • Year and Date
      2014-08-26
    • Related Report
      2014 Research-status Report
  • [Funded Workshop] Collaboration among mathematics, engineering and industry on various problems in infrastructure and environment2016

    • Place of Presentation
      九州大学MI研究所
    • Year and Date
      2016-10-25
    • Related Report
      2016 Annual Research Report
  • [Funded Workshop] Mathematical Backgrounds and Future Progress of Practical Inverse Problems2015

    • Place of Presentation
      九州大学MI研究所
    • Year and Date
      2015-11-10
    • Related Report
      2015 Research-status Report

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Published: 2014-04-04   Modified: 2018-03-22  

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