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Research in problems related to the Radon transform

Research Project

Project/Area Number 22540214
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic 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) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
KeywordsRadon変換 / 非破壊検査 / 超局所解析 / 逆問題 / 認証理論 / ラドン変換 / CTスキャン / コンクリート建造物 / 積分幾何 / 佐藤超関数 / 流体力学 / 指紋認証 / 生産関数
Research Abstract

With support of this research fund, I have organized four conferenceses in inverse problems and microlocal analysis, which promoted research exchanges between the reserchers in inverse problems and in microlocal analysis, which also established the industry-academia collaboration system between industry, mathematics and engineering in order to develop new technologies in non-destructive testings.
Throughout this research, we have created new research tasks to develop new technologies in non-destructive testings which will be very important for revitalization of obsolescent infrastructures. We have achieved several partial results on these research tasks from the viewpoints of practice and theory.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (30 results)

All 2014 2013 2012 2011 2010

All Journal Article (6 results) (of which Peer Reviewed: 3 results) Presentation (24 results) (of which Invited: 10 results)

  • [Journal Article] An inverse problem to detect an inclusion in a homogeneous medium by the Dirichlet to Dirichlet data for the heat equation2014

    • Author(s)
      Takashi Takiguchi and Ryusei Yamashita
    • Journal Title

      MI Lecute Note

      Volume: 54 Pages: 77-93

    • URL

      http://gcoe-mi.jp/temp/publish/780e338a272694d92babed9b2fa35e0c.pdf

    • Related Report
      2013 Final Research Report
  • [Journal Article] An inverse problem to detect an inclusion in a homogeneous medium by the Dirichlet to Dirichlet data for the heat equation2014

    • Author(s)
      Takashi TAKIGUCHI and Ryusei YAMASHITA
    • Journal Title

      MI Lecture Note

      Volume: 54 Pages: 77-93

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
  • [Journal Article] On the Structure of Hyperfunctions and Ultradistributions2013

    • Author(s)
      Takashi Takiguchi
    • Journal Title

      数理解析研究所講究録

      Volume: 1861 Pages: 71-82

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1861-08.pdf

    • Related Report
      2013 Annual Research Report 2013 Final Research Report 2012 Annual Research Report
  • [Journal Article] Non-uniqueness of the reconstruction for connected and simply connected sets2012

    • Author(s)
      Takashi Takiguchi
    • Journal Title

      Acta Matematica Scientia

      Volume: 32B Pages: 1637-1646

    • Related Report
      2013 Final Research 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
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-uniqueness of the reconstruction for connected and simply connected setsin the plane by their fixed finite projections2012

    • Author(s)
      Takashi Takiguchi
    • Journal Title

      Acta Mathematica Scientia

      Volume: 132 no.3(To appear)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] How G.N. Hounsfield practicalized the computerized tomography2014

    • Author(s)
      Takashi Takiguchi
    • Organizer
      復旦大学数学科学学院学術報告会
    • Place of Presentation
      復旦大学(中華人民共和国)
    • Year and Date
      2014-03-11
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] An inverse problem of the heat equation for practical application2014

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Colloquium at Sogang University
    • Place of Presentation
      Sogang University (大韓民国)
    • Year and Date
      2014-02-06
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] How the computerized tomography was practicalized2014

    • Author(s)
      Takashi Takiguchi
    • Organizer
      日本数式処理学会東北地区合同分科会
    • Place of Presentation
      仙台カルチャーセンター
    • Year and Date
      2014-01-26
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] How the computerized tomography was practicalized2014

    • Author(s)
      Takashi TAKIGUCHI
    • Organizer
      日本数式処理学会 東北地区合同分科会
    • Place of Presentation
      仙台青葉カルチャーセンター
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] An inverse problem of the heat equation for practical application2014

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Colloquium at Sogang University
    • Place of Presentation
      Sogang University (Korea)
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] How G.N. Hounsfield practicalized the computerized tomography2014

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Colloquium at Fudan University
    • Place of Presentation
      Fudan University (China)
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] An inverse problem to detect an inclusion in a homogeneous medium by the Dirichlet to Dirichlet data for the heat equation2013

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Inverse problems for practice, the present and the future
    • Place of Presentation
      九州大学IMI研究所
    • Year and Date
      2013-09-04
    • Related Report
      2013 Final Research Report
  • [Presentation] Non-destructive testing for mixed materials of the two kinds and integral geometry2013

    • Author(s)
      Takashi Takiguchi
    • Organizer
      ミニシンポジウム「建造物の構造解析における非破壊検査と逆問題」
    • Place of Presentation
      防衛大学校
    • Year and Date
      2013-07-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Remarks on the representation of the vortex sheets in perfect fluid2013

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Recent development of theory of analytic functionals and releated topics
    • Place of Presentation
      北海道大学
    • Year and Date
      2013-03-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Vortex sheets in perfect fluid and hyperfunctions2013

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Applied Analysis Seminar
    • Place of Presentation
      Ewha Womens University (大韓民国)
    • Year and Date
      2013-02-14
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Non-destructive testing for mixed materias of the two kinds and integral geometry2013

    • Author(s)
      Takashi TAKIGUCHI
    • Organizer
      建造物の構造解析における非破壊検査と逆問題
    • Place of Presentation
      防衛大学校
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
  • [Presentation] An inverse problem to detect an inclusion in a homogeneous media by the Dirichlet to Dirichlet data for the heat equation2013

    • Author(s)
      Takashi TAKIGUCHI
    • Organizer
      Invese problems for practice, the present and the future
    • Place of Presentation
      九州大学IMI研究所
    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
  • [Presentation] On the structure of hyperfunctions and ultradistributions2012

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Recent development of microlocal analysis and asymptotic analysis
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-10-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Structure for subclasses of hyperfunctions and unique continuation property2012

    • Author(s)
      Takashi Takiguchi
    • Organizer
      埼玉大学理学部数学教室談話会
    • Place of Presentation
      埼玉大学理学部数学教室
    • Year and Date
      2012-10-19
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On Fourier hyperfunctions and ultradistributions2012

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Microlocal Analysis, Differential Equations and Related Topics
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2012-08-02
    • Related Report
      2013 Final Research Report
  • [Presentation] On uniqueness problems for the Radon transform2012

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Colloquium at KAIST
    • Place of Presentation
      KAIST (大韓民国)
    • Year and Date
      2012-02-03
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On uniqueness problem for the Radon transform2012

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Colloquium at KAIST
    • Place of Presentation
      KAIST(韓国)(invited talk)(招待講演)
    • Year and Date
      2012-02-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] On the representation of the vortex sheets in fluid mechanics2012

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Colloquium at Sogang University
    • Place of Presentation
      Sogang University (大韓民国)
    • Year and Date
      2012-02-02
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On the representation of the vortex sheets in fluid mechanics2012

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Seminar on Applied Analysis at Sogang University
    • Place of Presentation
      Sogang University(韓国)(invited talk)(招待講演)
    • Year and Date
      2012-02-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] Unique continuation of microlocally analytic functions and their structure2011

    • Author(s)
      Takashi Takiguchi
    • Organizer
      国際研究集会"Microlocal Analysis and Related Topics"
    • Place of Presentation
      埼玉大学東京ステーションカレッジ(東京都)
    • Year and Date
      2011-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Unique continuation of microlocally analytic functions and their structure2011

    • Author(s)
      Takashi Takiguchi
    • Organizer
      Microlocal Analysis and Related Topics
    • Place of Presentation
      埼玉大学東京ステーションカレッジ
    • Year and Date
      2011-12-11
    • Related Report
      2013 Final Research Report
  • [Presentation] 超局所一意接続性と超函数の構造について2010

    • Author(s)
      Takashi Takiguchi
    • Organizer
      日本数学会2010年度秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-23
    • Related Report
      2013 Final Research Report
  • [Presentation] 超局所一意接続性と超函数の構造について2010

    • Author(s)
      滝口孝志
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-09-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] An inverse problem for the Schr\"odinger equation and the X ray transform2010

    • Author(s)
      滝口孝志
    • Organizer
      研究集会「偏微分方程式の逆問題解析とその周辺分野に関する研究」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2010-06-23
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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