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Chigira Hiroaki  千木良 弘朗

ORCIDConnect your ORCID iD *help
… Alternative Names

CHIGIRA Hiroaki  千木良 弘朗

千木良 弘明  チギラ ヒロアキ

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Researcher Number 30447122
Other IDs
Affiliation (Current) 2025: 東北大学, 経済学研究科, 准教授
Affiliation (based on the past Project Information) *help 2016 – 2018: 東北大学, 経済学研究科, 准教授
2012 – 2015: 東北大学, 経済学研究科(研究院), 准教授
2014: 東北大学, 大学院経済学研究科, 准教授
2007 – 2012: Tohoku University, 大学院・経済学研究科, 准教授
2007: 東北大学, 経済学研究科, 准教授
Review Section/Research Field
Principal Investigator
Economic statistics
Except Principal Investigator
Economic statistics
Keywords
Principal Investigator
パネルデータ / 経済統計学 / 計量経済学
Except Principal Investigator
計量経済学 / 人口統計 / 標本調査 / 小地域統計 / 経済統計 / 政府統計 / パネルデータ分析 … More / 国際情報交流 / 家計調査の改善と応用 / 標本調査票 / 人口予測 / 統計の秘匿 / 地域統計 / SNA / 匿名化 / パネル・データ / パネルデータ / 季節調整 / データの匿名化 / ミクロ経済データ / 政府公表系列 / マクロ時系列 / GDP統計 / 季節調整法 / ベンチマーク法 / ベンチマーク問題 / 季節調節法 / ミクロ統計データ / マクロ時系列データ / 数理統計学 / 東アジア金融市場 / 東アジア経済協力 / 東アジア産業構造 / 共変動 / 非定常時系列 / 共和分 / 東アジア債権市場 / 東アジア債券市場 / 多変量 GARCH モデル / 非線形時系列モデル / 東アジア金融協力 / ラグ変数追加法 / ラグ変数追加 / 正規近似 / 定数項除去法 / 単位根検定 / パネル分析 / 統計数学 / 経済統計学 / 収益率分散 / 事前情報 / 直交回帰説明変数 / 分散推定 / ベイズ計量経済学 / 分散構造未知 / ホワイトのHCCM / MCMC / 分散不均一性 / マルコフ連鎖モンテカルロ法 / ベイズ Less
  • Research Projects

    (6 results)
  • Research Products

    (55 results)
  • Co-Researchers

    (17 People)
  •  Proposals for economic and official statistics in the perspective of theoretical statistics and applications

    • Principal Investigator
      Yamamoto Taku
    • Project Period (FY)
      2015 – 2018
    • Research Category
      Grant-in-Aid for Scientific Research (A)
    • Research Field
      Economic statistics
    • Research Institution
      Hitotsubashi University
      The Institute of Statistical Research
  •  Theoretical Foundations and Applications of Economic and Official Statistics

    • Principal Investigator
      YAMAMOTO Taku
    • Project Period (FY)
      2011 – 2014
    • Research Category
      Grant-in-Aid for Scientific Research (A)
    • Research Field
      Economic statistics
    • Research Institution
      Nihon University
  •  Examination of East Asian Economic and Financial Cooperation by Using Nonlinear Time Series Models

    • Principal Investigator
      TSUKUDA Yoshihiko
    • Project Period (FY)
      2010 – 2012
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Economic statistics
    • Research Institution
      Tohoku University
  •  Econometric Analysis of the Panel Unit Root : Case Where Cross Section Dimension is Finite

    • Principal Investigator
      YAMAMOTO Taku
    • Project Period (FY)
      2008 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Economic statistics
    • Research Institution
      Nihon University
  •  Bayesian Estimation of Unknown Regression Error Heteroscedasticity

    • Principal Investigator
      SHIBA Tsunemasa
    • Project Period (FY)
      2007 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Economic statistics
    • Research Institution
      Hitotsubashi University
  •  A STATISTICAL INFERENCE WITH GOOD SMALL SAMPLE PERFORMANCES IN DYNAMIC PANEL DATA MODELSPrincipal Investigator

    • Principal Investigator
      CHIGIRA Hiroaki
    • Project Period (FY)
      2007 – 2008
    • Research Category
      Grant-in-Aid for Young Scientists (B)
    • Research Field
      Economic statistics
    • Research Institution
      Tohoku University

All 2019 2018 2017 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 Other

All Journal Article Presentation Book

  • [Book] 動学的パネルデータ分析2011

    • Author(s)
      千木良弘朗・早川和彦・山本拓
    • Total Pages
      338
    • Publisher
      知泉書館
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Book] 動学的パネルデータ分析2011

    • Author(s)
      千木良弘朗、早川和彦、山本拓
    • Total Pages
      338
    • Publisher
      知泉書館
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Book] 動学的パネルデータ分析2011

    • Author(s)
      千木良弘朗,早川和彦,山本拓
    • Total Pages
      325
    • Publisher
      知泉書館
    • Data Source
      KAKENHI-PROJECT-22530205
  • [Book] 動学的パネルデータ分析2011

    • Author(s)
      千木良弘明
    • Total Pages
      350
    • Publisher
      知泉書院
    • Data Source
      KAKENHI-PROJECT-22530205
  • [Journal Article] Evaluation of Statistical Methods for Forecasting Mortality: The Lee-Carter Method and Its Alternative2014

    • Author(s)
      Taku Yamamoto,Hiroaki Chigira and Chisako Yamamoto
    • Journal Title

      Proceedings of the 59th World Statistics Conference

      Volume: 59th Pages: 3506-3511

    • Data Source
      KAKENHI-PROJECT-23243039
  • [Journal Article] The Effect of Estimating Parameters on Long-term Forecasts for Cointegrated Systems2012

    • Author(s)
      Chigira,H. Yamamoto,T.
    • Journal Title

      Journal of Forecating

      Volume: 31 Pages: 344-360

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-22530205
  • [Journal Article] The Effect of Estimating Parameters onLong-Term Forecasts for CointegratedSystems2012

    • Author(s)
      Chigira, H. and Taku, Y
    • Journal Title

      Journal of Forecasting

      Volume: Vol. 31, No.4 Issue: 4 Pages: 344-360

    • DOI

      10.1002/for.1230

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-22530205, KAKENHI-PROJECT-23243039
  • [Journal Article] 小標本特性に優れたパネル単位根検定2011

    • Author(s)
      千木良弘朗, 山本拓
    • Journal Title

      Tohoku Economics Research Group Discussion Paper

      Volume: 268 Pages: 17-17

    • NAID

      120005261198

    • Data Source
      KAKENHI-PROJECT-23243039
  • [Journal Article] Bayesian Estimation of Unknown Regression Error Hetero scedasticity2009

    • Author(s)
      Hiroaki Chigira, Tsunemasa Shiba
    • Journal Title

      CFEE Discussion Paper Series #2008-2

      Pages: 1-27

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] Bayesian Estimation of Unknown Regression Error Hetero scedasticity2009

    • Author(s)
      Hiroaki Chigira, Tsunemasa Shiba
    • Journal Title

      Global COE Hi-Stat Discussion Paper Series #051

      Pages: 1-27

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] Forecasting in Large Cointegrated Systems2009

    • Author(s)
      Hiroaki Chigira, Taku Yamamoto
    • Journal Title

      Journal of Forecasting 26

      Pages: 631-650

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] Forecasting in Large Cointegrated Systems2009

    • Author(s)
      千木良弘朗, 山本拓
    • Journal Title

      Journal of Forecasting Vol.26

      Pages: 631-650

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] Bayesian Estimation of Unknown Regression Error Heteroscedasticity2009

    • Author(s)
      Hiroaki Chigira and Tsunemasa Shiba
    • Journal Title

      Institute of Economic Research, Hitotsubashi University #51

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] 非定常な動学的パネル分析 : 展望2008

    • Author(s)
      早川和彦, 千木良弘朗, 山本拓
    • Journal Title

      経済研究 59

      Pages: 126-138

    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] A Test of Cointegration Rank Based on Principal Component Analysis2008

    • Author(s)
      Hiroaki Chigira
    • Journal Title

      Applied Economics Letters 15

      Pages: 693-696

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] A Test of Cointegration Rank Based on Principal Component Analysis2008

    • Author(s)
      Hiroaki Chigira
    • Journal Title

      Applied Economics Letters Volume 15

      Pages: 693-696

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19730156
  • [Journal Article] 静学的パネルデータ分析-概観-2008

    • Author(s)
      千木良弘朗
    • Journal Title

      経済研究 Vol.59

      Pages: 97-11

    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] 非定常な動学的パネル分析2008

    • Author(s)
      早川 和彦,千木良 弘朗,山本 拓
    • Journal Title

      経済研究 第59巻

      Pages: 126-138

    • Data Source
      KAKENHI-PROJECT-19730156
  • [Journal Article] 静学的パネルデータ分析-概観-2008

    • Author(s)
      千木良 弘朗
    • Journal Title

      経済研究 第59巻

      Pages: 97-111

    • Data Source
      KAKENHI-PROJECT-19730156
  • [Journal Article] A Test of Cointegration Rank Based on Principal Component Analysis2008

    • Author(s)
      千木良弘朗
    • Journal Title

      Applied Economics Letters Vol.15

      Pages: 693-696

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] 静学的パネルデータ分析-概観-2008

    • Author(s)
      千木良弘朗
    • Journal Title

      経済研究 59

      Pages: 97-111

    • Data Source
      KAKENHI-PROJECT-19730156
  • [Journal Article] 非定常な動学的パネル分析2008

    • Author(s)
      早川和彦、千木良弘朗、山本拓
    • Journal Title

      展望、経済研究 Vol.59

      Pages: 126-138

    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] 非定常な動学的パネル分析2008

    • Author(s)
      早川和彦, 千木良弘朗, 山本拓
    • Journal Title

      経済研究 59

      Pages: 126-138

    • Data Source
      KAKENHI-PROJECT-19730156
  • [Journal Article] 静学的パネルデータ分析-概観-2008

    • Author(s)
      千木良弘朗
    • Journal Title

      経済研究 59

      Pages: 97-111

    • Data Source
      KAKENHI-PROJECT-20530177
  • [Journal Article] A Test of Cointegration Rank Based on Principal Component Analysis2008

    • Author(s)
      Hiroaki Chigira
    • Journal Title

      Applied Economics Letters 15

      Pages: 693-696

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19730156
  • [Journal Article] Bayesian Estimation of Unknown Regression Error Heteroscedasticity2007

    • Author(s)
      Hiroaki Chigira and Tsunemasa Shiba
    • Journal Title

      Institute of Economic Research, Hitotsubashi University No.221

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] Bayesian Estimation of Unknown Regression Error Heteroscedasticity2007

    • Author(s)
      Hiroaki Chigira and Tsunemasa Shiba
    • Journal Title

      Hi-Stat Discussion Paper #221

      Pages: 1-20

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] Finite Sample Modifications of the Granger Non-Causality Test in Cointegrated Vector Autoregressions2007

    • Author(s)
      Hiroaki Chigira and Taku Yamamoto
    • Journal Title

      Communications in Statistics-Theory and Methods Volume 36

      Pages: 981-1003

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19730156
  • [Journal Article] 構造を仮定しない不均一分散の推定2006

    • Author(s)
      千木良弘, 朗斯波恒正
    • Journal Title

      一橋経済学 第1巻,第1号

      Pages: 1-13

    • NAID

      110007622480

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] Bayesian Estimation of Unknown Heteroscedastic Variances2006

    • Author(s)
      Hiroaki Chigira and Tsunemasa Shiba
    • Journal Title

      Institute of Economic Research, Hitotsubashi University No.185

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] 構造を仮定しない不均一分散の推定(注 : 創刊号の巻頭論文)2006

    • Author(s)
      千木良 弘朗, 斯波 恒正
    • Journal Title

      一橋経済学 1

      Pages: 1-13

    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] Equivalence of Two Expressions of the Impact Matrix

    • Author(s)
      Kurozumi, E., Chigira, H. and Yamamoto,T
    • Journal Title

      Econometric Theory vol.21, No.4

      Pages: 870-875

    • NAID

      120000823627

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19530178
  • [Journal Article] A Test of Serial Independence of Deviations from Cointegrating Relations

    • Author(s)
      Chigira, H
    • Journal Title

      Economics Letters vol.92, No.1

      Pages: 52-57

    • NAID

      120006933875

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19530178
  • [Presentation] Statistical Inference in Regression Models with Possibly Integrated Processes2019

    • Author(s)
      千木良 弘朗、 山本 拓
    • Organizer
      科学研究プロジェクト「経済統計・政府統計の理論と応用」研究集会
    • Data Source
      KAKENHI-PROJECT-15H01943
  • [Presentation] GMM When Regressors are Exogenous2018

    • Author(s)
      Yamamoto Taku、Chigira Hiroaki
    • Organizer
      23rd International Conference on Computational Statistics (Compstat 2018)
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15H01943
  • [Presentation] Forecasting mortality: Some recent developments2017

    • Author(s)
      Yamamoto, T., and Chigira, H.
    • Organizer
      83rd International Atlantic Economic Conference
    • Place of Presentation
      Berlin, Germany
    • Year and Date
      2017-03-22
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15H01943
  • [Presentation] 真のデータに線形制約がある際の観測誤差の修正-国民経済計算の場合2017

    • Author(s)
      千木良 弘朗, 山本 拓
    • Organizer
      カンファレンス「経済統計・政府統計の理論と応用」
    • Place of Presentation
      東京大学経済学部
    • Data Source
      KAKENHI-PROJECT-15H01943
  • [Presentation] Forecasting Mortality: Some Recent Developments2017

    • Author(s)
      Yamamoto Tkau、Chigira Hiroaki
    • Organizer
      IISES 33rd International Academic Conference
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-15H01943
  • [Presentation] 観測誤差と線形制約を伴う真のデータの推定に関する新たな近接法2015

    • Author(s)
      千木良 弘朗, 山本 拓
    • Organizer
      研究集会「経済統計・政府統計の数理的基礎と応用2014」
    • Place of Presentation
      東京大学(東京都文京区)
    • Year and Date
      2015-01-31
    • Data Source
      KAKENHI-PROJECT-23243039
  • [Presentation] Evaluation of Statistical Methods for Forecasting Mortality: The Lee-Carter Method and Its Alternative2013

    • Author(s)
      Taku Yamamoto,Hiroaki Chigira and Chisako Yamamoto
    • Organizer
      59th World Statistics Congress
    • Place of Presentation
      Hong Kong Convention and Exhibition Centre ( Hong Kong,China)
    • Data Source
      KAKENHI-PROJECT-23243039
  • [Presentation] Lee-Carter予測に関する時系列分析の理論的な長所と短所の解明と代替的予測法の提案2012

    • Author(s)
      千木良弘朗,山本拓
    • Organizer
      研究集会「経済統計・政府統計の数理的基礎と応用2012」
    • Place of Presentation
      青森公立大学
    • Year and Date
      2012-09-28
    • Data Source
      KAKENHI-PROJECT-22530205
  • [Presentation] Lee-Carter予測に関する時系列分析の理論的な長所と短所の解明と代替的予測法の提案2012

    • Author(s)
      千木良 弘朗, 山本 拓
    • Organizer
      研究集会「経済統計・政府統計の数理的基礎と応用2012」
    • Place of Presentation
      青森公立大学 (青森市)
    • Data Source
      KAKENHI-PROJECT-23243039
  • [Presentation] Lee-Carter予測に関する時系列分析の理論的視点からの評価と代替案2012

    • Author(s)
      千木良 弘朗, 山本 拓.
    • Organizer
      『わが国の長寿化の要因と社会・経済に与える影響に関する人口学的研究』研究会
    • Place of Presentation
      国立社会保障・人口問題研究所
    • Data Source
      KAKENHI-PROJECT-23243039
  • [Presentation] A New Test for a Unit Root in Dynamic Heterogeneous Panel Data Models2011

    • Author(s)
      Chigira, Hiroaki, Yamamoto, Taku
    • Organizer
      58^<th> World Congress of the International Statistical Institute
    • Place of Presentation
      Dublin, Ireland
    • Year and Date
      2011-08-23
    • Data Source
      KAKENHI-PROJECT-23243039
  • [Presentation] The Effect of Estimating Parameters on Long-Term Forecasts for Cointegrated Systems2010

    • Author(s)
      千木良弘朗, 山本拓
    • Place of Presentation
      パリ
    • Year and Date
      2010-08-24
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Presentation] Cointegration, Integration and Long-term Forecasting2009

    • Author(s)
      Hiroaki Chigira, Taku Yamamoto
    • Organizer
      4^<th> Japanese-European Bayesian Econometrics and Statistics Meeting
    • Place of Presentation
      バルセロナ(スペイン)
    • Year and Date
      2009-08-23
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Presentation] Cointegration, Integration and Long-term Forecasting2009

    • Author(s)
      千木良弘朗, 山本拓
    • Organizer
      4th Japanese-European Bayesian Econometrics and Statistics Meeting
    • Place of Presentation
      バルセロナ
    • Year and Date
      2009-08-23
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Presentation] Cointegration, Integration, and Long-term Forecasting2009

    • Author(s)
      山本拓, 千木良弘朗
    • Organizer
      67th International Atlantic Economic Conference
    • Place of Presentation
      ローマ
    • Year and Date
      2009-03-12
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Presentation] Bayesian Estimation of Unknown Regression Error Heteroscedasticity2008

    • Author(s)
      Tsunemasa Shiba, Hiroaki Chigira
    • Organizer
      2008 Far Eastern and South Asian Meeting of the Econometric Society
    • Place of Presentation
      シンガポール
    • Year and Date
      2008-07-16
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Presentation] Bayesian Estimation of Unknown Regression Error Heteroscedasticity2008

    • Author(s)
      Tsunemasa Shiba and Hiroaki Chigira
    • Organizer
      2008 Far Eastern and South Asian Meeting of the Econometric Society
    • Place of Presentation
      Singapore Management University
    • Year and Date
      2008-07-17
    • Data Source
      KAKENHI-PROJECT-19730156
  • [Presentation] Bayes ian Estimation of Unknown Regression Error Heteroscedasticity2008

    • Author(s)
      Tsunemasa Shiba, Hiroaki Chigira
    • Organizer
      2008 Far Eastern and South Asian Meeting of the Econometrio Society
    • Place of Presentation
      シンガポール
    • Year and Date
      2008-07-16
    • Data Source
      KAKENHI-PROJECT-20530177
  • [Presentation] Far Eastern Econometric Society Meeting2008

    • Author(s)
      Hiroaki Chigira and Tsunemasa Shiba
    • Organizer
      Singapore Management University
    • Place of Presentation
      Singapore
    • Year and Date
      2008-07-17
    • Data Source
      KAKENHI-PROJECT-19530178
  • [Presentation] 動学的パネル分析の計量理論:展望2007

    • Author(s)
      千木良 弘朗,早川 和彦,山本 拓
    • Organizer
      経済研究所定例研究会
    • Place of Presentation
      一橋大学
    • Year and Date
      2007-11-21
    • Data Source
      KAKENHI-PROJECT-19730156
  • [Presentation] LEE-Carte予測に関する時系列分析の理論的な長所と短所の解明

    • Author(s)
      千木良弘朗・山本拓
    • Organizer
      研究集会「経済統計・政府統計の数理的基礎と応用2012」
    • Place of Presentation
      青森公立大学
    • Data Source
      KAKENHI-PROJECT-22530205
  • [Presentation] Forecasting Mortality: Some Analytical, Experimental and Empirical Evidences

    • Author(s)
      Taku Yamamoto, Hiroaki Chigira, Chisako Yamamoto
    • Organizer
      21th International Conference on Computational Statistics
    • Place of Presentation
      The International Conference Centre Geneva, Geneve (Switherland)
    • Year and Date
      2014-08-19 – 2014-08-22
    • Data Source
      KAKENHI-PROJECT-23243039
  • 1.  YAMAMOTO Taku (50104716)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 23 results
  • 2.  UNAYAMA Suguru (20348840)
    # of Collaborated Projects: 3 results
    # of Collaborated Products: 0 results
  • 3.  KUNITOMO Naoto (10153313)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 4.  KAWASAKI Yoshinori (70249910)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 5.  TSUCHIYA Takahiro (00270413)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 6.  HOSHINO Nobuaki (00313627)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 7.  KUBOKAWA Tatsuya (20195499)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 8.  SATO Seishou (60280525)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 9.  TAKAOKA Makoto (60376663)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 10.  SHIBA Tsunemasa (90187386)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 9 results
  • 11.  TSUKUDA Yoshihiko (10091836)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 12.  HIOKI Shiro (80312528)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 13.  川崎 茂 (40631304)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 14.  早川 和彦 (00508161)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 15.  金子 隆一 (30415814)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 16.  大森 裕浩 (60251188)
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 17.  HAYASHI Masayoshi
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results

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