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量子・熱ゆらぎを考慮した生体分子高次系クラスターの理論的解明

Publicly Offered Research

Project AreaMolecular Science for Supra Functional Systems ? Development of Advanced Methods for Exploring Elementary Process
Project/Area Number 22018024
Research Category

Grant-in-Aid for Scientific Research on Priority Areas

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionYokohama City University

Principal Investigator

立川 仁典  横浜市立大学, 生命ナノシステム科学研究科, 教授 (00267410)

Co-Investigator(Kenkyū-buntansha) 北 幸海  横浜市立大学, 生命ナノシステム科学研究科, 助教 (40453047)
志賀 基之  日本原子力研究開発機構, システム計算科学センター, 研究員 (40370407)
高柳 敏幸  埼玉大学, 理工学研究科, 教授 (90354894)
Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2011: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2010: ¥2,000,000 (Direct Cost: ¥2,000,000)
Keywords水和機構 / 化学物理 / クラスター / 経路積分 / 生体分子
Research Abstract

これまで我々は、温度効果だけでなく水素原子核の量子揺らぎを考慮した多成分系分子理論を開発し、常温においても核の量子効果が重要であることを見出し、低障壁水素結合系における特徴的なNMRスペクトルの存在を理論的に予測してきた。本年度は主に以下を実施した。
(1)高次系への拡張:計算コストを抑えるために、マルチリゾリューション法に基づくポテンシャル曲面や、半経験的分子軌道法を適用した[1]。
(2)イオン水和クラスターの計算:Ag+(H2O)n(n=1-4)およびCu+(H20)の構造と振動スペクトルをより精密に算出するために、ab initio分子動力学(MD)法、ab initio経路積分分子動力学(PIMD)法[2]、ab initioリングポリマー分子動力学(RPMD)法を応用した。MD法およびRPMD法により得られた振動スペクトルは非調和性を考慮することができる。そのため、特にRPMD法で得られた振動スペクトルは、スケール因子を用いることなく実験値とよい一致を示した。
(3)生体小分子:ポルフィセンの二重プロトン移動機構の解析:photoactive yellow protein(PYP)の発光素(CRO)近傍における低障壁水素結合部位に、電子と原子核の量子性を考慮可能な多成分系密度汎関数理論を適用した。その結果、CROと隣接酸素原子間の距離が実験値とよい一致を示し、また重水素置換によって酸素原子間距離が伸張することを見出した。
[1]S.Sugawara, T.Yoshikawa, T.Takayanagi, and M.Tachikawa, Chem. Phys. Lett., 501, 238-244(2011).
[2]A.Koizumi, K.Suzuki, M.Shiga, and M.Tachikawa, J. Chem. Phys.(Communication), 134, 031101(3pages) (2011).

Current Status of Research Progress
Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

電子状態(立川)と統計化学(志賀)だけでなく、新たに化学動力学(高柳)、分子力場(北)、さらにはポテンシャル曲面作成(八木)という多方面からの理論化学的アプローチを取入れ、有機的な共同研究を実施することで、当初計画以上の成果を得ることができた。さらには、関谷グループ(九大)や片岡グループ(奈良先端大)といった実験グループとの議論を通し、本領域内での共同研究も実施することができた。

Strategy for Future Research Activity

量子・熱ゆらぎを考慮した生体分子高次系クラスターを理論的に解明するためには、例えば溶媒を充分に含めた大規模計算等が必要である。本研究で構築した共同研究体制を積極的に発展させていくことで、さらなる生体分子高次系クラスターの理論解析を発展させていきたい。

Report

(2 results)
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (55 results)

All 2012 2011 2010 Other

All Journal Article (46 results) (of which Peer Reviewed: 46 results) Presentation (7 results) Remarks (2 results)

  • [Journal Article] Vibrational enhancement of positron affinities for nonpolar carbon dioxide and carbon disulfide molecules : Multi-component molecular orbital study for vibrational excited states2012

    • Author(s)
      K.Koyanagi, Y.Kita, M.Tachikawa
    • Journal Title

      Int.J.Quant.Chem.

      Volume: (in press)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Temperature dependence of self-assembled molecular capsules consisting of gear-shaped amphiphile molecules with molecular dynamics simulations2012

    • Author(s)
      J.Koseki, Y.Kita, S.Hiraoka, U.Nagashima, M.Tachikawa
    • Journal Title

      Int.J.Quant.Chem.

      Volume: (in press)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bound states of positron with simple carbonyl and aldehyde species with configuration interaction multi-component molecular orbital and local vibrational approaches2012

    • Author(s)
      M.Tachikawa, Y.Kita, R.J.Buenker
    • Journal Title

      New J.Phys.

      Volume: 14

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Systematic theoretical investigation of positron-binding to amino acid molecules with ab initio multi-component molecular orbital approach2012

    • Author(s)
      K.Koyanagi, Y.Kita, M.Tachikawa
    • Journal Title

      Eur.Phys.J.D.

      Volume: (in press)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum tautomerization in porphycene and its isotopomers : Path-integral molecular dynamics simulations2012

    • Author(s)
      T.Yoshikawa, S.Sugawara, T.Takayanagi, M.Shiga, M.Tachikawa
    • Journal Title

      Chem.Phys.

      Volume: 394 Pages: 46-51

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Real Wave Packet and Flux Analysis Studies of the H+F_2->HF+F Reaction"2012

    • Author(s)
      F.Gogtas, E.Karabulut, T.Takayanagi, T.Tanaka, R.Tutuk
    • Journal Title

      Int.J.Quantum.Chem.

      Volume: (in press)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fixed-node quantum Monte Carlo for molecule2012

    • Author(s)
      立川仁典, 北幸海
    • Journal Title

      巨大分子系の計算化学

      Volume: (in Japanese) Pages: 34-38

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 陽電子束縛化合物の第一原理計算2012

    • Author(s)
      立川仁典, 北幸海
    • Journal Title

      日本物理学会誌

      Volume: 67(in Japanese) Pages: 33-36

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytical optimization of orbital exponents in Gaussian-type functions for molecular systems based on MCSCF and MP2 levels of fully variational molecular orbital method2011

    • Author(s)
      N.Shimizu, T.Ishimoto, M.Tachikawa
    • Journal Title

      Theor.Chem.Acc.

      Volume: 130 Pages: 679-685

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Role of CH-pi interaction energy in self-assembled gear-shaped amphiphile molecules : Correlated ab initio molecular orbital and density functional theory study2011

    • Author(s)
      J.Koseki, Y.Kita, S.Hiraoka, U.Nagashima, M.Tachikawa
    • Journal Title

      Theor.Chem.Acc.

      Volume: 130 Pages: 1055-1059

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Proton Transfer in Hydrated Sulfuric Acid Clusters : A Perspective from Semiempirical Path Integral Simulations2011

    • Author(s)
      S.Sugawara, T.Yoshikawa, T.Takayanagi, M.Shiga, M.Tachikawa
    • Journal Title

      J.Phys.Chem.A.

      Volume: 115 Pages: 11486-11494

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isotope effect of proton and deuteron adsorption site on Zeolite-Templated carbon using path integral molecular dynamics2011

    • Author(s)
      K.Suzuki, M.Tachikawa, H.Ogawa, S.Ittisanronnachai, H.Nishihara, T.Kyotani, U.Nagashima
    • Journal Title

      Theor.Chem.Acc.

      Volume: 130 Pages: 1039-1042

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nuclear quantum effect on the hydrogen-bonded structure of guanine-cytosine pair2011

    • Author(s)
      M.Daido, A.Koizumi, M.Shiga, M.Tachikawa
    • Journal Title

      Theor.Chem.Acc.

      Volume: 130 Pages: 385-391

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ab initio quantum Monte Carlo study of the binding of a positron to alkali-metal hydrides2011

    • Author(s)
      Y.Kita, R.Maezono, M.Tachikawa, M.Towler, R.J.Needs
    • Journal Title

      J.Chem.Phys.

      Volume: 135

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ab initio path integral simulation of AgOH(H_2O)2011

    • Author(s)
      A.Koizumi, K.Suzuki, M.Shiga, M.Tachikawa
    • Journal Title

      Int.J.Quant.Chem.

      Volume: 112 Pages: 136-139

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical study of the reversible photoconversion mechanism in Dronpa2011

    • Author(s)
      J.Koseki, Y.Kita, U.Nagashima, M.Tachikawa
    • Journal Title

      Procedia Comput.Sci.

      Volume: 4 Pages: 251-260

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Molecular dynamics simulation for irreversible feature of green fluorescent protein before and after photoactivation2011

    • Author(s)
      J.Koseki, Y.Kita, M.Tachikawa
    • Journal Title

      Chem.Lett.

      Volume: 40 Pages: 476-477

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ab initio quantum chemical study on the mechanism of exceptional behavior of lysine for ion yields in MALDI-Role of vibrational entropic contribution in thermally averaged proton affinities-2011

    • Author(s)
      M.Hatakeyama, M.Tachikawa
    • Journal Title

      J.Mass Spectrometry

      Volume: 46 Pages: 376-382

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Path integral molecular dynamics for hydrogen adsorption site of zeolite-templated carbon with semi-empirical PM3 potential2011

    • Author(s)
      K.Suzuki, M.Kayanuma, M.Tachikawa, H.Ogawa, H.Nishihara, T.Kyotani, U.Nagashima
    • Journal Title

      Comp.Theor.Chem.

      Volume: 975 Pages: 128-133

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nuclear quantum effect on the dissociation energies of cationic hydrogen clusters2011

    • Author(s)
      M.Sugimoto, M.Shiga, M.Tachikawa
    • Journal Title

      Comp.Theor.Chem.

      Volume: 975 Pages: 31-37

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical investigations of nuclear quantum effect on molecular magnetic properties based on multi-component density functional theory2011

    • Author(s)
      Y.Kita, M.Tachikawa
    • Journal Title

      Comp.Theor.Chem.

      Volume: 975 Pages: 9-12

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A concerted mechanism between protron transfer of Zundel anion and displacement of counter cation2011

    • Author(s)
      A.Koizumi, K.Suzuki, M.Shiga, M.Tachikawa
    • Journal Title

      J.Chem.Phys.(communication)

      Volume: 134

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical study on mechanisms of structural rearrangement and ionic dissociation in the HCl(H_2O)_4 cluster with path-integral molecular dynamics simulations2011

    • Author(s)
      S.Sugawara, T.Yoshikawa, T.Takayanagi, M.Tachikawa
    • Journal Title

      Chem.Phys.Lett.

      Volume: 501 Pages: 238-244

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bound states of positron with nitrile species with configuration interaction multi-component molecular orbital approach2011

    • Author(s)
      M.Tachikawa, Y.Kita, R.J.Buenker
    • Journal Title

      Phys.Chem.Chem.Phys.

      Volume: 13 Pages: 2701-2705

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nuclear quantum effect on hydrogen adsorption site of zeolite-templated carbon model using path integral molecular dynamics2011

    • Author(s)
      K.Suzuki, M.Kayanuma, M.Tachikawa, H.Ogawa, H.Nishihara, T.Kyotani, U.Nagashima
    • Journal Title

      J.Alloys and Compounds

      Volume: 509S

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 新しい分子物理化学の確立-ポジトロニクス(陽電子技術)にむけて2011

    • Author(s)
      立川仁典, 北幸海
    • Journal Title

      化学(最新のトピックス)

      Volume: 66(in Japanese) Pages: 68-69

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bound states of positron with nitrile species with configuration interaction multi-component molecular orbital approach.2011

    • Author(s)
      M.Tachikawa, Y.Kita, R.J.Buenker
    • Journal Title

      Phys.Chem.Chem.Phys.

      Volume: 13 Pages: 2701-2705

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical study on mechanisms of structural rearrangement and ionic dissociation in the HCl(H_2O)_4 cluster with path-integral molecular dynamics simulations.2011

    • Author(s)
      S.Sugawara, T.Yoshikawa, T.Takayanagi, M.Tachikawa
    • Journal Title

      Chem.Phys.Lett.

      Volume: 501 Pages: 238-244

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nuclear quantum effect on the dissociation energies of cationic hydrogen clusters.2011

    • Author(s)
      M.Sugimoto, M.Shiga, M.Tachikawa
    • Journal Title

      Comp.Theor.Chem.

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A concerted mechanism between protron transfer of Zundel anion and displacement of counter cation.2011

    • Author(s)
      A.Koizumi, K.Suzuki, M.Shiga, M.Tachikawa
    • Journal Title

      J.Chem.Phys.(communication)

      Volume: 134

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Path integral molecular dynamics for hydrogen adsorption site of zeolite-templated carbon with semi-empirical PM3 potential.2011

    • Author(s)
      K.Suzuki, M.Kayanuma, M.Tachikawa, H.Ogawa, H.Nishihara, T.Kyotani, U.Nagashima
    • Journal Title

      Comp.Theor.Chem.

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ab initio quantum chemical study on the mechanism of exceptional behavior of lysine for ion yields in MALDI-Role of vibrational entropic contribution in thermally averaged proton affinities-.2011

    • Author(s)
      M.Hatakeyama, M.Tachikawa
    • Journal Title

      J.Mass Spectrometry

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical investigations of nuclear quantum effect on molecular magnetic properties based on multi-component density functional theory.2011

    • Author(s)
      Y.Kita, M.Tachikawa
    • Journal Title

      Comp.Theor.Chem.

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Molecular dynamics simulation for irreversible feature of green fluorescent protein before and after photoactivation.2011

    • Author(s)
      J.Koseki, Y.Kita, M.Tachikawa
    • Journal Title

      Chem.Lett.

      Volume: 40 Pages: 476-477

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical study of the reversible photoconversion mechanism in Dronpa.2011

    • Author(s)
      J.Koseki, Y.Kita, U.Nagashima, M.Tachikawa
    • Journal Title

      Procedia Comput.Sci.

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ab initio path integral simulation of AgOH(H_2O).2011

    • Author(s)
      A.Koizumi, K.Suzuki, M.Shiga, M.Tachikawa
    • Journal Title

      Int.J.Quant.Chem.

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Systematic Improvement of Energy-Components by Simultaneous Optimization of Exponents and Centers of Gaussian-Type Function Basis Sets for Molecular Self-Consistent-Field Wave Functions.2010

    • Author(s)
      T.Ishimoto, M.Tachikawa
    • Journal Title

      J.Comp.Chem.Jpn.

      Volume: 9 Pages: 1-8

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimized Molecular Exponents on Gaussian Basis Sets for Hybrid Orbitals of Hydrocarbon Molecules.2010

    • Author(s)
      T.Ishimoto, M.Tachikawa
    • Journal Title

      J.Comp.Chem.Jpn.

      Volume: 9 Pages: 15-20

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Geometric Isotope Effect on Low Barrier Hydrogen-Bonding Systems of Acetic Acid Dimer, Formic Acid Dimer, and Their Anionic Clusters by Using the Multi-Component Molecular Orbital Method.2010

    • Author(s)
      M.Kaneko, T.Udagawa, M.Tachikawa
    • Journal Title

      J.Comp.Chem.Jpn.

      Volume: 9 Pages: 21-28

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Formation of Schiff-base for photoreaction mechanism of red shift of GFP spectra.2010

    • Author(s)
      J.Koseki, Y.Kita, M.Tachikawa
    • Journal Title

      Biophys.Chem.

      Volume: 147 Pages: 140-145

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Efficient ab initio path integral hybrid Monte Carlo based on the fourth-order Trotter expansion : Application to fluoride ion-water cluster.2010

    • Author(s)
      K.Suzuki, M.Tachikawa, M.Shiga
    • Journal Title

      J.Chem.Phys.

      Volume: 132

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The chemical shift of deprotonated water dimer : Ab initio path integral simulation.2010

    • Author(s)
      M.Shiga, K.Suzuki, M.Tachikawa
    • Journal Title

      J.Chem.Phys.

      Volume: 132

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] First-principles calculation and transmission electron microscopy observation for hydrogen adsorption on carbon nanowalls.2010

    • Author(s)
      Y.Kita, S.Hayashi, I.Kinoshita, M.Tachibana, M.Tachikawa, K.Kobayashi, M.Tanimura
    • Journal Title

      J.Appl.Phys.

      Volume: 108

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theoretical study on the mechanism of double proton transfer in porphycene by path-integral molecular dynamics simulations.2010

    • Author(s)
      T.Yoshikawa, S.Sugawara, T.Takayanagi, M.Shiga, M.Tachikawa
    • Journal Title

      Chem.Phys.Lett.

      Volume: 496 Pages: 14-19

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Variational Monte Carlo Study of Positronic Compounds Using Inhomogeneous Backflow Transformations.2010

    • Author(s)
      Y.Kita, M.Tachikawa, N.D.Drummond, R.J.Needs
    • Journal Title

      Chem.Lett.

      Volume: 39 Pages: 1136-1137

    • NAID

      10027315042

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nuclear quantum effect on hydrogen adsorption site of zeolite-templated carbon model using path integral molecular dynamics2010

    • Author(s)
      K.Suzuki, M.Kayanuma, M.Tachikawa, H.Ogawa, H.Nishihara, T.Kyotani, U.Nagashima
    • Journal Title

      J.Alloys and Compounds

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Bound states of positron with nitrile species with several multi-component molecular theories2012

    • Author(s)
      Masanori Tachikawa
    • Organizer
      International Workshop on Positrons in Astrophysics
    • Place of Presentation
      Murren, Switzerland
    • Year and Date
      2012-03-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] "Multi component molecular theory for hydrogen bonded systems and positronic compounds2012

    • Author(s)
      Masanori Tachikawa
    • Organizer
      The 4th French-Japanese Workshop on Computational Methods in Chemistry
    • Place of Presentation
      Fukuoka, Japan(招待講演)
    • Year and Date
      2012-03-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] First-principles Calculations for Positron-attached Molecules2012

    • Author(s)
      Masanori Tachikawa
    • Organizer
      The Sixth General Meeting of ACCMS-VO
    • Place of Presentation
      Sendai, Japan(招待講演)
    • Year and Date
      2012-02-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] Multi component molecular theory for hydrogen bonded systems and positronic compounds2011

    • Author(s)
      Masanori Tachikawa
    • Organizer
      XVIth International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XVI)
    • Place of Presentation
      Kanazawa, Ishikawa(招待講演)
    • Year and Date
      2011-09-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] Path Integral simulation for Hydrogen Bonded Systems : Protonic Quantum Nature and H/D Isotope Effect2011

    • Author(s)
      Masanori Tachikawa
    • Organizer
      14th Asian Chemical Congress
    • Place of Presentation
      Bangkok, Thailand(招待講演)
    • Year and Date
      2011-09-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Multi component molecular theory for hydrogen bonded systems and positronic compounds2011

    • Author(s)
      Masanori Tachikawa
    • Organizer
      7th Congress of the International Society for Theoretical Chemical Physics (ISTCP-VII)
    • Place of Presentation
      Waseda, Tokyo
    • Year and Date
      2011-09-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Path integral simulation for hydrogen bonded systems : Protonic quantum nature and H/D isotope effect2011

    • Author(s)
      Masanori Tachikawa
    • Organizer
      ISOTOPES2011
    • Place of Presentation
      Provence-Alpes-Cote d'Azur, FRANCE(招待講演)
    • Year and Date
      2011-06-22
    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www-user.yokohama-cu.ac.jp/~tachi/

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://www-user.yokohama-cu.ac.jp/~tachi/

    • Related Report
      2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2018-03-28  

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