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Applications of Reproducing kernel theory and its new development in engineering and medical science

Research Project

Project/Area Number 26400192
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionGunma University

Principal Investigator

Matsuura Tsutomu  群馬大学, 大学院理工学府, 准教授 (80181692)

Co-Investigator(Kenkyū-buntansha) 齋藤 三郎  群馬大学, その他部局等, 名誉教授 (10110397)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords再生核理論 / 逆問題 / 数値計算 / 正則化 / 積分方程式 / アルゴリズム / 離散化 / 再生核 / ゼロ除算
Outline of Final Research Achievements

We developed a new type of Tikhonov regularization combined with the theory of reproducing kernels. Using our method of regularization we have challenged some famous and historically difficult inverse problems. Furthermore we constructed concrete algorithms for solving those problems and confirmed their effectiveness by numerical experiments. Especially, we tried new approach to the field of medical science. Specifically, we published 2 papers and presented 3 papers in Medical Sciences (Microscopic Image of Podocyte and Cochlear cells) and we published 9 papers and presented 18 papers in Mathematical Sciences (general reproducing kernels and division by zero).

Report

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

    (36 results)

All 2017 2016 2015 2014

All Journal Article (9 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Open Access: 7 results,  Acknowledgement Compliant: 4 results) Presentation (22 results) (of which Int'l Joint Research: 5 results,  Invited: 2 results) Book (5 results)

  • [Journal Article] Relations of 0 and ∞2017

    • Author(s)
      H. Okumura, S. Saitoh and T. Matsuura
    • Journal Title

      Journal of Technology and Social Science

      Volume: 1 Pages: 70-77

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Division by Zero z/0 = 0 in Euclidean Spaces2017

    • Author(s)
      H. Michiwaki, H. Okumura and S. Saitoh
    • Journal Title

      International Journal of Mathematics and Computation

      Volume: 9 Pages: 1-16

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Matrices and division by zero z/0=02016

    • Author(s)
      T. Matsuura and S. Saitoh
    • Journal Title

      Advances in Linear Algebra and Matrix Theory,

      Volume: 6 Issue: 02 Pages: 51-58

    • DOI

      10.4236/alamt.2016.62007

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Solutions of Tikhonov Functional Equations and Applications to Multiplication Operators on Szego Spaces2016

    • Author(s)
      L. P. Castro1, S. Saitoh, A. Yamada
    • Journal Title

      Complex Analysis and Operator Theory

      Volume: - Issue: 8 Pages: 1705-1723

    • DOI

      10.1007/s11785-016-0545-4

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 腎糸球体足細胞画像からの細胞体の抽出とシグナル調節タンパク質αと糖尿病による細胞変性識別の試み2015

    • Author(s)
      元川 嵩介,松浦 勉,青木 武生
    • Journal Title

      Medical Imaging Technology

      Volume: 33 Pages: 208-216

    • NAID

      130005110537

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A Fundamental Theorem on Initial Value Problems by Using the Theory of Reproducing Kernels2015

    • Author(s)
      L. P. Castro; M. M. Rodrigues; S. Saitoh
    • Journal Title

      Complex Anal. Oper. Theory

      Volume: 9 Issue: 1 Pages: 87-98

    • DOI

      10.1007/s11785-014-0375-1

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case2015

    • Author(s)
      Castro, L. P.; Rojas, E. M.; Saitoh, S.; Tuan, N. M.; Tuan, P. D.
    • Journal Title

      Anal. Appl.

      Volume: 13 Issue: 01 Pages: 1-22

    • DOI

      10.1142/s0219530514500468

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Initial Value Problems in Linear Integral Operator Equations2014

    • Author(s)
      L.P. Castro, M.M. Rodrigues and S. Saitoh
    • Journal Title

      Springer Optimization and Its Applications

      Volume: 94 Pages: 175-188

    • DOI

      10.1007/978-3-319-06554-0_7

    • ISBN
      9783319065533, 9783319065540
    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Bessel differential heat initial value problem in a reproducing kernel Hilbert space framework2014

    • Author(s)
      L.P. Castro, M.M. Rodrigues and S. Saitoh
    • Journal Title

      AIP - Conf. Proc.

      Volume: 1637 Pages: 165-170

    • DOI

      10.1063/1.4904575

    • Related Report
      2014 Research-status Report
  • [Presentation] The general sampling theory by using reproducing kernels2017

    • Author(s)
      齋藤三郎,藤原宏志
    • Organizer
      日本数学会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] log 0 = log1 = 0 and applications2017

    • Author(s)
      齋藤三郎,道脇裕
    • Organizer
      日本数学会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] A fundamental theorem on initial value problems by using the theory of reproducing kernels2017

    • Author(s)
      齋藤三郎,P. L. Castro, M. M. Rodrigues
    • Organizer
      日本数学会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] Division by zero z/0=0 and differential equations2017

    • Author(s)
      齋藤三郎,S. Pinelas
    • Organizer
      日本数学会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] 糸球体上皮細胞画像における足突起領域の自動抽出2016

    • Author(s)
      元川嵩介, 松浦勉
    • Organizer
      International Conference on Advanced Engineering and Its Education in 2016
    • Place of Presentation
      Kiryu Chamber of Commerce and Industry, Keivick Hall
    • Year and Date
      2016-10-13
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Division by zero z/0=0 in Euclidean spaces2016

    • Author(s)
      齋藤三郎, 道脇裕,奥村博
    • Organizer
      日本数学会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] Matrices and division by zero z/0=02016

    • Author(s)
      齋藤三郎,松浦勉
    • Organizer
      日本数学会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] Solutions of Tikhonov functional equations and applications to multiplication operators on Szege spaces2016

    • Author(s)
      齋藤三郎,山田陽,Luis. P. Castro
    • Organizer
      日本数学会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] Division by zero z/0=0 in complex analysis (draft)2016

    • Author(s)
      齋藤三郎,高木正子
    • Organizer
      日本数学会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] Reality of the division by zero z/0 = 02016

    • Author(s)
      齋藤三郎, 道脇裕, 山田正人
    • Organizer
      日本数学会 春季大会
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
  • [Presentation] The concept of divisions (fractionals) in fields containing the division by zero2016

    • Author(s)
      齋藤三郎, 山田正人
    • Organizer
      日本数学会 春季大会
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
  • [Presentation] A method for automatic extraction of foot process region from podocyte image2016

    • Author(s)
      T. Matsuura, S. Motokawa, T. Matsuzaki, K. Hiromura and T. Aoki
    • Organizer
      GUMI & AMDE2016
    • Place of Presentation
      Kiryu City Performance Arts Center
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Image classification of podocyte by neural network2015

    • Author(s)
      T. Matsuura, S. Motokawa, T. Matsuzaki, K. Hiromura, and T. Aoki
    • Organizer
      2nd International Symposium of Gunma University Medical Innovation
    • Place of Presentation
      刀城会館(前橋)
    • Year and Date
      2015-12-08
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Aveiro discretization method in mathematics: A new discretization principle (I: Principle)2015

    • Author(s)
      齋藤三郎, L. P. Castro, 藤原宏志, M. M. Rodrigues, Vu Kim Tuan
    • Organizer
      日本数学会 秋季大会
    • Place of Presentation
      京都産業大学(京都市北区)
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Aveiro discretization method in mathematics: A new discretization principle (II: Applications)2015

    • Author(s)
      齋藤三郎, L. P. Castro, 藤原宏志, M. M. Rodrigues, Vu Kim Tuan
    • Organizer
      日本数学会 秋季大会
    • Place of Presentation
      京都産業大学(京都市北区)
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] General integral transforms by the concept of generalized reproducing kernels2015

    • Author(s)
      Tsutomu Matsuura, Saburou Saitoh
    • Organizer
      ISAAC (The International Society for Analysis, its Applications and Computation) 2015
    • Place of Presentation
      Macau (China)
    • Year and Date
      2015-08-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] What are reproducing kernels? Generalized reproducing kernels and generalized delta functions2015

    • Author(s)
      Saburou Saitoh, Yoshihiro Sawano
    • Organizer
      ISAAC (The International Society for Analysis, its Applications and Computation) 2015
    • Place of Presentation
      Macau (China)
    • Year and Date
      2015-08-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] General integral transforms by the concept of generalized reproducing kernels2015

    • Author(s)
      Tsutomu Matsuura
    • Organizer
      International Society for Analysis, its Applications and Computation
    • Place of Presentation
      マカオ(中国)
    • Year and Date
      2015-08-02 – 2015-08-08
    • Related Report
      2014 Research-status Report
  • [Presentation] New meanings of the division by zero and interpretations on 100/0=0 and 0/0=02015

    • Author(s)
      M. Kuroda, H. Michiwaki, S. Saitoh, M. Yamane
    • Organizer
      日本数学会
    • Place of Presentation
      明治大学(東京都千代田区)
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] A new concept for the point at infinity and the division by zero z/0=0 (note).2015

    • Author(s)
      H. Michiwaki, S. Saitoh, and M. Takagi,
    • Organizer
      日本数学会
    • Place of Presentation
      明治大学(東京都千代田区)
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] 糸球体上皮細胞の走査電子顕微鏡画像による形態解析2015

    • Author(s)
      松浦勉 元川嵩介
    • Organizer
      医理工生命医科学融合医療イノベーションプロジェクト成果報告会
    • Place of Presentation
      群馬大学理工学部(群馬県桐生市)
    • Year and Date
      2015-03-20
    • Related Report
      2014 Research-status Report
  • [Presentation] Extract local area from microscopic image and quantify shape of region2014

    • Author(s)
      松浦勉 元川嵩介
    • Organizer
      International Symposium of Gunma University Medical Innovation
    • Place of Presentation
      桐生市市民文化会館(群馬県桐生市)
    • Year and Date
      2014-12-05
    • Related Report
      2014 Research-status Report
  • [Book] Theory of Reproducing Kernels and Applications (Developments in Mathematics)2016

    • Author(s)
      S. Saitoh and Y. Sawano
    • Total Pages
      452
    • Publisher
      Springer
    • Related Report
      2016 Annual Research Report
  • [Book] Current Trends in Analysis and Its Applications2015

    • Author(s)
      M.M. Rodrigues and S. Saitoh
    • Total Pages
      892
    • Publisher
      Birkhaeser
    • Related Report
      2015 Research-status Report 2014 Research-status Report
  • [Book] Current Trends in Analysis and Its Applications2015

    • Author(s)
      L.P. Castro, H. Fujiwara, M.M. Rodrigues, S. Saitoh, and V.K. Tuan
    • Total Pages
      892
    • Publisher
      Birkhaeser
    • Related Report
      2015 Research-status Report 2014 Research-status Report
  • [Book] Current Trends in Analysis and Its Applications2015

    • Author(s)
      T. Matsuura and S. Saitoh
    • Total Pages
      892
    • Publisher
      Birkhaeser
    • Related Report
      2015 Research-status Report
  • [Book] Current Trends in Analysis and Its Applications2015

    • Author(s)
      T. Matsuura and S. Saitoih
    • Total Pages
      892
    • Publisher
      Birkhaeser
    • Related Report
      2014 Research-status Report

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

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