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Development of an advanced method for nonlinear eigenvalue problems and its applications

Research Project

Project/Area Number 25286097
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Computational science
Research InstitutionUniversity of Tsukuba

Principal Investigator

SAKURAI Tetsuya  筑波大学, システム情報系, 教授 (60187086)

Co-Investigator(Kenkyū-buntansha) 多田野 寛人  筑波大学, システム情報系, 助教 (50507845)
今倉 暁  筑波大学, システム情報系, 助教 (60610045)
池上 努  国立研究開発法人産業技術総合研究所, 情報技術研究部門, 研究員 (80245612)
Research Collaborator FUTAMURA Yasunori  
MAEDA Yasuyuki  
CHEN Hongjia  
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥17,680,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥4,080,000)
Fiscal Year 2015: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2014: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2013: ¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Keywordsアルゴリズム / 高性能計算 / 大規模計算 / 非線形固有値問題 / 基盤ソフトウェア / 非線型固有値問題
Outline of Final Research Achievements

In this project, we considered a numerical algorithm for nonlinear eigenvalue problems that can be applied to large-scale problems in various application areas of computational sciences. We studied theoretical aspects and some related techniques of a contour integral-based eivensolver for nonlinear eigenvalue problems to apply for various practical applications in computational sciences. According to the results, we developed a method for a spectral projection method using contour integral. We also developed some methods and related techniques to attain high performance and high reliability on large-scale cluster machines. We evaluated the efficiency of the method with some applications. We implemented our method on a function CISS in the software library for the solution of large scale sparse eigenvalue problems on parallel computers SLEPc that is developing at Universitat Politecnica de Valencia.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • Research Products

    (54 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (5 results) Journal Article (16 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 16 results,  Acknowledgement Compliant: 10 results,  Open Access: 4 results) Presentation (33 results) (of which Int'l Joint Research: 8 results,  Invited: 1 results)

  • [Int'l Joint Research] バレンシア工科大学(スペイン)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] マンチェスター大学(英国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] 国立台湾大学(台湾)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] 西北工業大学(中国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] ヴッパータール大学(ドイツ)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Improving the numerical stability of the Sakurai-Sugiura method for quadratic eigenvalue problems2017

    • Author(s)
      Hongjia Chen, Yasuyuki Maeda, Akira Imakura, Tetsuya Sakurai, Francoise Tisseur
    • Journal Title

      JSIAM Letters

      Volume: 9 Pages: 17-20

    • NAID

      130005475943

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reduced-Shifted Conjugate-Gradient Method for a Green’s Function: Efficient Numerical Approach in a Nano-Structured Superconductor2017

    • Author(s)
      Yuki Nagai, Yasushi Shinohara, Yasunori Futamura, and Tetsuya Sakurai
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 86 Issue: 1 Pages: 014708-014708

    • DOI

      10.7566/jpsj.86.014708

    • NAID

      40021057702

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Solving large-scale nonlinear eigenvalue problems by rational interpolation and resolvent sampling based Rayleigh-Ritz method2017

    • Author(s)
      J. Xiao, C. Zhang, TM. Huang and T. Sakurai
    • Journal Title

      Int. J. Numer. Methods Eng.

      Volume: 110 Issue: 8 Pages: 776-800

    • DOI

      10.1002/nme.5441

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Relationships among contour integral-based methods for solving generalized eigenvalue problems2016

    • Author(s)
      A. Imakura, L. Du and T. Sakurai,
    • Journal Title

      Japan J. Indust. Appl. Math.

      Volume: 33 Issue: 3 Pages: 721-750

    • DOI

      10.1007/s13160-016-0224-x

    • NAID

      210000183673

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Highly parallel computation of generalized eigenvalue problem in vibration for automatic transmission of vehicles using the Sakurai-Sugiura method and supercomputers2016

    • Author(s)
      T. Ide, Y. Inoue, Y. Futamura and T. Sakurai
    • Journal Title

      Math. Anal. Continuum Mech. Indust. Appl.

      Volume: 26 Pages: 207-218

    • DOI

      10.1007/978-981-10-2633-1_16

    • ISBN
      9789811026324, 9789811026331
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Error bounds of Rayleigh--Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems2016

    • Author(s)
      Akira Imakura, Lei Du, Tetsuya Sakurai
    • Journal Title

      Numerical Algorithms

      Volume: 71 Pages: 103-120

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Recovering from accuracy deterioration in the contour integral-based eigensolver2016

    • Author(s)
      Tetsuya Hasegawa, Akira Imakura, Tetsuya Sakurai
    • Journal Title

      JSIAM Letters

      Volume: 8 Issue: 0 Pages: 1-4

    • DOI

      10.14495/jsiaml.8.1

    • NAID

      130005125234

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Filter analysis for the stochastic estimation of eigenvalue counts2015

    • Author(s)
      Yasuyuki Maeda, Yasunori Futamura, Akira Imakura, Tetsuya Sakurai
    • Journal Title

      JSIAM Letters

      Volume: 7 Issue: 0 Pages: 53-56

    • DOI

      10.14495/jsiaml.7.53

    • NAID

      130005087644

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Improving the convergence behaviour of BiCGSTAB by applying <i>D</i>-norm minimization2015

    • Author(s)
      Lijiong Su, Akira Imakura, Hiroto Tadano, Tetsuya Sakurai
    • Journal Title

      JSIAM Letters

      Volume: 7 Issue: 0 Pages: 37-40

    • DOI

      10.14495/jsiaml.7.37

    • NAID

      130005068708

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Improvement of the accuracy of the approximate solution of the Block BiCR method2014

    • Author(s)
      H. Tadano, Y. Ishikawa, and A. Imakura
    • Journal Title

      JSIAM Letters

      Volume: 6 Issue: 0 Pages: 61-64

    • DOI

      10.14495/jsiaml.6.61

    • NAID

      130004706457

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] An efficient algorithm to construct an orthonormal basis for the extended Krylov subspace2014

    • Author(s)
      Akira Imakura
    • Journal Title

      East Asian Journal on Applied Mathematics

      Volume: 4 Issue: 3 Pages: 267-282

    • DOI

      10.4208/eajam.240413.020614a

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems2014

    • Author(s)
      Akira Imakura, Lei Du, Tetsuya Sakurai
    • Journal Title

      Applied Mathematics Letters

      Volume: 32 Pages: 22-27

    • DOI

      10.1016/j.aml.2014.02.007

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Numerical Construction of a Low-Energy Effective Hamiltonian in a Self-Consistent Bogoliubov-de Gennes Approach of Superconductivity2013

    • Author(s)
      Yuki Nagai, Yasushi Shinohara, Yasunori Futamura, Yukihiro Ota. and Tetsuya Sakurai
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 32 Issue: 9 Pages: 0947011-10

    • DOI

      10.7566/jpsj.82.094701

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A projection method for nonlinear eigenvalue problems using contour integrals2013

    • Author(s)
      Shinnosuke Yokota, Tetsuya Sakurai
    • Journal Title

      JSIAM Letters

      Volume: 5 Issue: 0 Pages: 41-44

    • DOI

      10.14495/jsiaml.5.41

    • NAID

      130003371120

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Efficient parameter estimation and implementation of a contour integral-based eigensolver2013

    • Author(s)
      Tetsuya Sakurai, Yasunori Futamura and Hiroto Tadano
    • Journal Title

      J. Alg. Comput. Tech.

      Volume: 7 Pages: 249-269

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multi-GPU scalable implementation of a contour-integral-based eigensolver for real symmetric dense generalized eigenvalue problems2013

    • Author(s)
      T. Yano, Y. Futamura, T. Sakurai
    • Journal Title

      Proceedings of 8th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC-2013)

      Volume: 1 Pages: 121-127

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] 積分型固有値解法による大規模シミュレーションとデータ解析2016

    • Author(s)
      櫻井 鉄也
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学 筑波キャンパス(茨城県つくば市)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 2つのKrylov部分空間を利用した複素モーメント型固有値解法2016

    • Author(s)
      今倉 暁, 櫻井 鉄也
    • Organizer
      日本応用数理学会 第12回 研究部会連合発表会
    • Place of Presentation
      神戸学院大学 ポートアイランドキャンパス(兵庫県神戸市)
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Krylov subspace in complex moment-based eigensolver2016

    • Author(s)
      Akira Imakura
    • Organizer
      Workshop on Numerical Algebra, Algorithms, and Analysis
    • Place of Presentation
      National Institute of Informatics (NII), Tokyo
    • Year and Date
      2016-01-11
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A novel complex moment-based eigensolver using a communication-avoiding Arnoldi process2015

    • Author(s)
      Akira Imakura, Tetsuya Sakurai
    • Organizer
      SIAM Conference on Applied Linear Algebra (SIAM LA15)
    • Place of Presentation
      Hyatt Regency Atranta, Atranta, Georgia, USA
    • Year and Date
      2015-10-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Contour Integral-based Parallel Eigensolver with Higher Complex Moments2015

    • Author(s)
      Tetsuya Sakurai, Yasunori Futamura, Akira Imakura
    • Organizer
      SIAM Conference on Applied Linear Algebra (SIAM LA15)
    • Place of Presentation
      Hyatt Regency Atranta, Atranta, Georgia, USA
    • Year and Date
      2015-10-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Development of the Shifted Block BiCGGR method and accuracy improvement of approximate solutions2015

    • Author(s)
      Hiroto Tadano, Shusaku Saito, Akira Imakura
    • Organizer
      International Conference on Simulation Technology (JSST2015)
    • Place of Presentation
      Toyama International Conference Center(富山県富山市)
    • Year and Date
      2015-10-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 複数右辺ベクトル・複数シフトをもつ線形方程式に対するShifted Block Krylov部分空間法の近似解の精度改善2015

    • Author(s)
      多田野 寛人, 齋藤 周作, 今倉 暁
    • Organizer
      【プラズマ壁相互作用における非線形現象の理論モデル構築と画像・動画解析手法開発に関する研究会】第1回非線形・可視化部門研究会
    • Place of Presentation
      核融合科学研究所(岐阜県土岐市)
    • Year and Date
      2015-09-28
    • Related Report
      2015 Annual Research Report
  • [Presentation] Error resilience strategy of a complex moment-based eigensolver2015

    • Author(s)
      Akira Imakura, Yasunori Futamura, Tetsuya Sakurai
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2015)
    • Place of Presentation
      EPOCHAL TSUKUBA, Tsukuba-city,Ibaraki
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Accuracy improvement of the Shifted Block BiCGGR method for linear systems with multiple shifts and multiple right-hand sides2015

    • Author(s)
      Hiroto Tadano, Shusaku Saito, Akira Imakura
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2015)
    • Place of Presentation
      EPOCHAL TSUKUBA, Tsukuba-city,Ibaraki
    • Year and Date
      2015-09-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Arnoldi-type contour integral-based eigensolver for solving nonlinear eigenvalue problems2015

    • Author(s)
      Akira Imakura, Tetsuya Sakurai
    • Organizer
      ICIAM 2015
    • Place of Presentation
      Beijing, China
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 内部固有値問題のためのFEAST法に対するArnoldi/Lanczos型改良法の提案2015

    • Author(s)
      今倉 暁, 二村 保徳, 櫻井 鉄也
    • Organizer
      2015年並列/分散/協調処理に関する『別府』サマー・ワークショップ (SWoPP2015)
    • Place of Presentation
      ビーコンプラザ 別府国際コンベンションセンター(大分県別府市)
    • Year and Date
      2015-08-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] Shifted Block BiCGSTAB(l)法の構築とその近似解の精度について2015

    • Author(s)
      齋藤 周作, 多田野 寛人, 今倉 暁
    • Organizer
      第44回 数値解析シンポジウム (NAS2015)
    • Place of Presentation
      ぶどうの丘(山梨県甲州市)
    • Year and Date
      2015-06-08
    • Related Report
      2015 Annual Research Report
  • [Presentation] Inherent error resilience of a complex moment-based eigensolver for solving interior eigenvalue problem2015

    • Author(s)
      Akira Imakura, Yasunori Futamura, Tetsuya Sakurai
    • Organizer
      2015 LBNL - Tsukuba Joint Meeting
    • Place of Presentation
      LBNL, USA
    • Year and Date
      2015-05-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Fault tolerance inherent in a complex moment-based eigensolver2015

    • Author(s)
      Akira Imakura
    • Organizer
      Sparse Solvers for Exascale: From Building Blocks to Applications
    • Place of Presentation
      Greifswald (Germany)
    • Year and Date
      2015-03-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] Inherent Error Resilience of a Complex Moment-Based Eigensolver2015

    • Author(s)
      Akira Imakura
    • Organizer
      SIAM Conference on Computational Science and Engineering (CSE15)
    • Place of Presentation
      Salt Lake City (USA)
    • Year and Date
      2015-03-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] Error resilience strategy of a complex moment-based eigensolver2015

    • Author(s)
      Akira Imakura
    • Organizer
      Annual Meeting on Advanced Computing System and Infrastructure (ACSI) 2015
    • Place of Presentation
      つくば国際会議場(茨城県つくば市)
    • Year and Date
      2015-01-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] 各種周回積分型固有値解法の関係性について2014

    • Author(s)
      今倉暁, 杜 磊, 櫻井 鉄也
    • Organizer
      2014年度 RIMS 研究集会「新時代の科学技術を牽引する数値解析学」
    • Place of Presentation
      京都大学 数理解析研究所(京都府京都市)
    • Year and Date
      2014-10-08
    • Related Report
      2014 Annual Research Report
  • [Presentation] 実数計算のみを利用した周回積分型固有値解法における精度悪化とその対処2014

    • Author(s)
      長谷川 哲也
    • Organizer
      第8回協定講座シンポジウム
    • Place of Presentation
      神戸大学(兵庫県神戸市)
    • Year and Date
      2014-09-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] Communication-Avoiding Arnoldi版周回積分型固有値解法2014

    • Author(s)
      今倉暁, 杜 磊, 櫻井 鉄也
    • Organizer
      日本応用数理学会 2014年度年会
    • Place of Presentation
      政策研究大学院大学 (東京都港区)
    • Year and Date
      2014-09-03
    • Related Report
      2014 Annual Research Report
  • [Presentation] A Novel Contour Integral Based Eigensolver for Solving Linear and Nonlinear Eigenvalue Problems2014

    • Author(s)
      Akira Imakura, Tetsuya Sakurai
    • Organizer
      East Asia Section of SIAM (EASIAM) 2014
    • Place of Presentation
      Chonburi (Thailand)
    • Year and Date
      2014-06-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] Hankel行列版周回積分型固有値解法の精度解析2014

    • Author(s)
      今倉暁, 杜 磊, 長谷川 哲也, 櫻井 鉄也
    • Organizer
      第43回 数値解析シンポジウム -NAS2014-
    • Place of Presentation
      ホテル日航八重山(沖縄県石垣市)
    • Year and Date
      2014-06-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] On error resilience of a complex moment-based eigensolver2014

    • Author(s)
      Tetsuya Sakurai, Yasunori Futamura, Akira IMAKURA
    • Organizer
      10th International Workshop on Accurate Solution of Eigenvalue Problems (IWASEP10)
    • Place of Presentation
      Dubrovnik(クロアチア)
    • Year and Date
      2014-06-02
    • Related Report
      2014 Annual Research Report
  • [Presentation] A Contour Integral-Based Parallel Eigensolver for Nonlinear Eigenvalue Problems2014

    • Author(s)
      Tetsuya SAKURAI
    • Organizer
      Manchester Workshop on Nonlinear Eigenvalue Problems (NEP14)
    • Place of Presentation
      Manchester(UK)
    • Year and Date
      2014-04-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] A Novel Interpretation for the Contour Integral-Based Spectral Projection Methods for Solving Generalized Eigenvalues Problems

    • Author(s)
      Akira IMAKURA
    • Organizer
      The 9th East Asia SIAM Conference - The 2nd Conference on Industrial and Applied Mathematics
    • Place of Presentation
      The Newton Hotel (Indonesia)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 固有値分布推定による周回積分を用いた並列固有値解法パラメータ自動設定

    • Author(s)
      前田恭行
    • Organizer
      2013年並列/分散/協調処理に関する 『北九州』サマー・ワークショップ(SWoPP北九州2013)
    • Place of Presentation
      北九州国際会議場 (福岡)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 周回積分型固有値解法に対するBlock Arnoldi法に基づく新解釈および改良法の提案

    • Author(s)
      今倉暁
    • Organizer
      日本応用数理学会2013年度年会
    • Place of Presentation
      アクロス福岡 (福岡)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 周回積分を用いた固有値解法に基づく並列固有値解析エンジン

    • Author(s)
      二村保徳
    • Organizer
      日本応用数理学会2013年度年会
    • Place of Presentation
      アクロス福岡 (福岡)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Multi-GPU scalable implementation of a contour-integral-based eigensolver for real symmetric dense generalized eigenvalue problems

    • Author(s)
      T. Yano
    • Organizer
      8th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC-2013)
    • Place of Presentation
      Compiegne (France)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 周回積分型固有値解法に基づく並列固有値解析ソフトウェア

    • Author(s)
      今倉暁
    • Organizer
      今後の HPC(基盤技術と応用) に関するワークショップ
    • Place of Presentation
      長崎市図書館 (長崎)
    • Related Report
      2013 Annual Research Report
  • [Presentation] A Hierarchical Parallel Software Package of a Complex Moment Based Eigensolver

    • Author(s)
      Yasunori Futamura
    • Organizer
      SIAM Conference on Parallel Processing for Scientific Computing
    • Place of Presentation
      Marriott Portland Downtown Waterfromnt (USA)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Accuracy analysis on the Rayleigh-Ritz type of the contour integral based eigensolver

    • Author(s)
      Akira IMAKURA
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014)
    • Place of Presentation
      EPOCHAL TSUKUBA (Tsukuba)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Parallel Implementation of a Contour-Integral-Based Eigensolver for Dense Generalized Eigenvalue Problems on GPU Clusters

    • Author(s)
      T. Yano
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014)
    • Place of Presentation
      EPOCHAL TSUKUBA (Tsukuba)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Contour Integral Spectral Slicing Solver CISS in SLEPc

    • Author(s)
      Y. Maeda
    • Organizer
      International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014)
    • Place of Presentation
      EPOCHAL TSUKUBA (Tsukuba)
    • Related Report
      2013 Annual Research Report

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Published: 2013-05-21   Modified: 2023-03-16  

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