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Unitary Representations of Hyperfinite Heisenberg Groups and Their Applications to Quantum Physics

Research Project

Project/Area Number 08454039
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya University

Principal Investigator

OZAWA Masanao  School of Informatics and Sciences, Nagoya University, Prfessor, 情報文化学部, 教授 (40126313)

Co-Investigator(Kenkyū-buntansha) MORIMOTO Hiroshi  Graduate School of Human Informatics, Professor, 大学院・人間情報学研究科, 教授 (20115645)
MATSUBARA Yo  School of Informatics and Sciences, Associate Prfessor, 情報文化学部, 助教授 (30242788)
YASUMOTO Masahiro  Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (10144114)
SHINODA Juichi  Graduate School of Human Informatics, Professor, 大学院・人間情報学研究科, 教授 (30022685)
IHARA Shunsuke  School of Informatics and Sciences, Prfessor, 情報文化学部, 教授 (00023200)
伊藤 正之  名古屋大学, 情報文化学部, 教授 (60022638)
Project Period (FY) 1996 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥6,300,000 (Direct Cost: ¥6,300,000)
Fiscal Year 1998: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1997: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1996: ¥2,100,000 (Direct Cost: ¥2,100,000)
Keywordsnonstandard analysis / quantum optics / Heisenberg groups / canonical commutation relatins / unitary representations / hyperfinite / phase operators / quantizations / Heisenberg群 / 量子力学 / Schrodinger表現 / Z_1飽和的超準宇宙 / 超準殻 / 作用素測度 / Naimark拡大 / Hilberk■間
Research Abstract

This is an interdisciplinary research including foundations of mathematics, applied analysis, mathematical physics, and quantum mechanics. The representation theory of hyperfinite Heisenberg groups was instituted by Ojima and Ozawa in 1992 in order to give a unified framework for systematic applications of nonstandard analysis to quantum physics. The research results include results in foundations of mathematics relative to the nonstandard method and also includes results in applied analysis concerning various applications. The following are of particular importance relative to applications to quantum physics. Kelemen and Robinson reconstructed the phi^4_2 model of Glimm and Jaffe with methods of nonstandard analysis. In order to apply nonstandard analysis to other constructions of field models systematically, we generalize their nonstandard analytical methods of representing the canonical commutation relations in the framework of the theory of nonstandard unitary representations. As applications, the following representations are reconstructed in this framework : the Segal representation, relativistic time zero fields, and the Araki-Woods representation. In the next application of a representation of a hyperfinite Heisenberg group, we constructed a self-adjoint phase operator of a single-mode electromagnetic field in quantum mechanics. This operator is naturally considered as the limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is shown to be a Naimark extension of the optimal probability operator-valued measure found by Helstrom. A recent text book on quantum optics mentions our result as follows : The calculation of phase using this operator is formally similar to that using the Pegg-Barnett operator and gives the correct result within infinitesimal error, so that the calculation of phase becomes rather easier than the Pegg-Barnett method.

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (99 results)

All Other

All Publications (99 results)

  • [Publications] M.Ozawa: "On the concept of wave packet reduction II: Operational approach" J.Japan Assoc.Phil.Sci.24. 9-15 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Phase operator problem and macroscopic extension of quantum mechanics" Ann.Phys.(N.Y.). 257. 65-83 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "An operational approach to quantum state reduction" Ann.Phys.(N.Y.). 259. 121-137 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum state reduction and the quantum Bayes principle" Quantum Communication, Computing, and Measurement(Plenum, New York, 1997). 233-241

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Incompleteness of the hyperreals: An application of forcing to nonstandard analysis" Mathematica Moravica,Special Volume. 125-140 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "On the concept of wave packet reduction III: Quantum disturbance" J.Japan Assoc.Phil.Sci.25. 25-31 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Comments on “Conceptual difference between wave packet reduction and reproducibility"" J.Japan Assoc.Phil.Sci.25. 55-57 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum nondemolition monitoring of universal quantum computers" Phys.Rev.Lett.80. 631-634 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum state reduction: An operational approach" Fortschr.Phys.46. 595-604 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa and H.Nishimura: "Computational complexity of quantum computers" Studies in Infor-matics and Sciences, Nagoya University. 8. 1-21 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "The problem of measurement and the theory of quantum state reduction" Fifth In-ternational Conference on Squeezed States and Uncertainty Relations (NASA, Goddard, 1988). 517-522

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum Turing machines: Local transition, Preparation, measurement, and halting" Proc.4th International Conference on Quantum Communication, Measurement and Computing. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "On the concept of quantum state reduction: Inconsistency of the orthodox view" Preprint Series in Mathematical Sciences, Nagoya University. 1998-2. 1-14 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Operational characterization of simultaneous measurements in quantum mechanics" Preprint Series in Mathematical Sciences, Nagoya University. 1998-3. 1-9 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Controlling quantum state reduction" Preprint Series in Mathematical Sciences, Nagoya University. 1998-4. 1-9 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Measurability and computability" Preprint Series in Mathematical Sciences, Nagoya University. 1998-9. 1-8 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Yamashita: "Hyperfinite-dimensinal representations of canonical commutation relation" J.Math.Phys.39. 2682-2692 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Yamashita and M.Ozawa: "Nonstandard representations of the canonical commutation relations" Preprint Series in Mathematical Sciences, Nagoya University. 1999-1. 1-18 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Mochizuki and J.Shinoda: "A note on the functions which are not polynomial time computable from their graphs" Ann.Japan Assoc.Phil.Sci.9. 17-21 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Shinoda: "Strong polynomial-time reducibility" Ann.Pure and Applied Logic. 84. 97-117 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Shinoda and T.A.Slaman: "Recursive in a generic real" Preprint Series in Mathematical Sciences, Nagoya University. 35. 1-9 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozaki and J.Shinoda: "On MOD_kP counting degrees" Math.Logic Quarterly. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Takeuti and M.Yasumoto: "Forcing on bounded arithmetic" Lecture Note in Logic. 6. 120-138 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Takeuti and M.Yasumoto: "Forcing on bounded arithmetic II" J.Symbolic Logic. 63. 860-868 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Burke and Y.Matsubara: "Ideals and combinatorial principles" J.symbolic logic. 62. 117-122 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Matsubara and M.Shioya: "Nowhere precipitousness of some ideals" J.symbolic logic. 63. 1003-1006 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 松原洋: "Non-Stationary ideal と universe of sets" 数学. 51. 18-33 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Burke and Y.Matsubara: "The extent of the strength in the club filters" Israel J.Math.(to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Yoshinobu: "On strength of precipitousness of some ideals and towers" J.Math.Soc.Japan. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara: "Some inequalities for channel capacities, mutual informations and mean-squared errors" IEEE Trans.Information Theory. IT-42. 1536-1540 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara and Y.Sakuma: "Signal detection in continuous time white Gaussian channel" Proc.Sev-enth Japan-Russia Symposium on Probability Theory and Mathematical Statistics(World Scientific,1996). 147-156

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara and J.Muramatsu: "On the converse theorem in hypothesis testing for stationary Gaussian sequences, Studies in Informatics and Sciences" Nagoya University. 5. 19-27 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara and M.Kubo: "The asymptotics of string matching probabilities for Gaussian random sequences" Preprint Series in Mathematical Sciences, Nagoya University. 1998-6. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara: "Information transmission over continuous-time Gaussian channels with feedback" Problems of Information Transmission. 35. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara: "Large deviation theorems for Gaussian processes and their applications in information theory" (to appear in a festshrift for T.Hida).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Morimoto: "A diffusion model for the evolution of metalloporphyrin" J.Math.Biol.34. 689-706 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Morimoto: "Evolutionary game theory with mutations for finite populations" Studies in Infor-matics and Sciences, Nagoya University. 5. 117-129 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Morimoto: "生物学における非線型数学モデル" Japan Assoc.Math.Biol., Newsletter. 21. 23-24 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Satoh: "Sums of products of two q-Bernoulli numbers" J.Number Theory. 74. 173-180 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Satoho: "A recurrence formula for the q-Bernoulli numbers attached to formal group" Nagoya Math.J. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kurimoto,H.N.Mondal,and T.Morisue: "Analysis of velocity and temperature fields of molten metal in DC electric arc furnace" J.Chem.Eng.Japan. 29. 75-81 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.N.Mondal,H.Kurimoto,and T.Morisue: "Analysis of electrically induced flows in DC electric arc furnace" IEEE Trans.Magnetics. 32. 1026-1029 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "On the concept of wave packet reduction II : Operational approach" J.Japan Assoc.Phil.Sci.24. 9-15 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Phase operator problem and macroscopic extension of quantum mechanics" Ann.Phys.(N.Y.). 257. 65-83 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "An operational approach to quantum state reduction" Ann.Phys.(N.Y.). 259. 121-137 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum state reduction and the quantum Bays principle" Quantum Communication, Computing, and Measurement (Plenum, New York, 1997). 233-241

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Incompleteness of the hyperreals : An application of forcing to nonstandard analysis" Mathematica Moravica. Special Volume. 125-140 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "On the concept of wave packet reduction III : Quantum disturbance" J.Japan Assoc.Phil.Sci.25. 25-31 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Comments on "Conceptual difference between wave packet reduction and reproducibility" J.Japan Assoc.Phil.Sci.25. 55-57 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum nondemolition monitoring of universal quantum computers" Phys.Rev.Lett.80. 631-634 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum state reduction : An operational approach" Fortschr.Phys.46. 595-604 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa and H.Nishimura: "Computational complexity of quantum computers" Studies in Informatics and Sciences, Nagoya University. 8. 1-21 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "The problem of measurement and the theory of quantum state reduction" Fifth In-ternational Conference on Squeezed States and Uncertainty Relations (NASA,Goddard, 1998). 517-522

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum Turing machines : Local transition, preparation, measurement, and halting" Proc.4th International Conference on Quantum Communication, Measurement and Computing. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "On the concept of quantum state reduction : Inconsistency of the orthodox view" Preprint Series in Mathematical Sciences, Nagoya University. 1998-2. 1-14 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Operational characterization of simultaneous measurements in quantum mechanics" Preprint Series in Mathematical Sciences, Nagoya University. 1998-3. 1-9 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Controlling quantum state reduction" Preprint Series in Mathematical Sciences, Nagoya University. 1998-4. 1-9 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Measurability and computability" Preprint Series in Mathematical Sciences, Nagoya University. 1998-9. 1-8 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Yamashita: "Hyperfinite-dimensinal representations of canonical commutation relation" J.Math.Phys.39. 2682-2692 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Yamashita and M.Ozawa: "Nonstandard representations of the canonical commutation relations" Preprint Series in Mathematical Sciences, Nagoya University. 1999-1. 1-18 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Mochizuki and J.Shinoda: "A note on the functions which are not polynomial time computable from their graphs" Ann.Japan Assoc.Phil.Sci.9. 17-21 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Shinoda: "Strong polynomial-time reducibility" Ann.Pure and Applied Logic. 84. 97-117 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Shinoda and T.A.Slaman: "Recursive in a generic real" Preprint Series in Mathematical Sciences, Nagoya University. 35. 1-9 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozaki and J.Shinoda: "On MOD_kP counting degrees" Math.Logic Quarterly. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Takeuti and M.Yasumoto: "Forcing on bounded arithmetic" Lecture Note in Logic. 6. 120-138 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] G.Takeuti and M.Yasumoto: "Forcing on bounded arithmetic II" J.Symbolic Logic. 63. 860-868 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Burke and Y.Matsubara: "Ideals and combinatorial principles" J.Symbolic Logic. 62. 117-122 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Matsubara and M.Shioya: "Nowhere precipitousness of some ideals" J.Symbolic Logic. 63. 1003-1006 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Matsubara: "Non-stationary ideals and the universe of sets" Suugaku (Mathematics). 51. 18-33 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] D.Burke and Y.Matsubara: "The extent of the strength in the club filters" Israel J.Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Y.Yoshinobu: "On strength of precipitousness of some ideals and towers" J.Math.Soc.Japan. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara: "Some inequalities for channel capacities, mutual informations and mean-squared errors, IEEE Trans." Information Theory. IT-42. 1536-1540 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara and Y.Sakuma: "Signal detection in continuous time white Gaussian channel" Proc.Sev-enth Japan-Russia Symposium on Probability Theory and Mathematical Statistics (World Scientific, 1996). 147-156

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara and J.Muramatsu: "On the converse theorem in hypothesis testing for stationary Gaussian sequences" Studies in Informatics and Sciences, Nagoya University. 5. 19-27 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara and M.Kubo: "The asymptotics of string matching probabilities for Gaussian random sequences" Preprint Series in Mathematical Sciences, Nagoya University. 1998-6. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara: "Information transmission over continuous-time Gaussian channels with feedback" Problems of Information Transmission. 35. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] S.Ihara: "Large deviation theorems for Gaussian processes and their applications in information theory" (to appear in a festshrift for T.Hida.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Morimoto: "A diffusion model for the evolution of metalloporphyrin" J.Math.Biol.34. 689-706 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Morimoto: "Evolutionary game theory with mutations for finite populations" Studies in Infor-matics and Sciences, Nagoya University. 5. 117-129 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Morimoto: "Non-linear mathematical models in biology" Japan Assoc.Math.Biol., Newsletter. 21. 23-24 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Satoh: "Sums of products of two q-Bernoulli numbers" J.Number Theory. 74. 173-180 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Satoh: "A recurrence formula for the q-Bernoulli numbers attached to formal group" Nagoya Math.J.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Kurimoto, H.N.Mondal, and T.Morisue: "Analysis of velocity and temperature fields of molten metal in DC electric arc furnace" J.Chem.Eng.Japan. 29. 75-81 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.N.Mondal, H.Kurimoto, and T.Morisue: "Analysis of electrically induced flows in DC electric arc furnace" IEEE Trans.Magnetics. 32. 1026-1029 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Ozawa: "Quantum State Reduction: An Operational Approach" Fortschr.Phys.46. 595-604 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Ozawa: "The Problem of Measurement and the Theroy of Quantum State Reduction" Fifth International Conference on Squeezed States and Uncertainty Relations. 517-522 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Yamashita: "Hyperfinie-dimensional representation of canonical commutation relation" J.Math.Phys.39. 2682-2692 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Matsubara: "Nowhere Precipitousmess of Some Ideals" J.Symbolic Logic. 63. 1003-1006 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] G.Takeuti: "Forcing on Bounded Arithmetic II" J.Symbolic Logic. 63. 860-868 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Ihara: "Information Transmission over Continuous-Time Gaussian Channels with Feedback" Problems of Information Transmission. 35. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Masanao Ozawa: "Phase Operator Problem and Macroscopic Extension of Quantum Mechanics" Annals of Physics. 257・1. 65-83 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Masanao Ozawa: "An Operational Approach to Quantum State Reduction" Annals of Physics. 259・1. 121-137 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Masanao Ozawa: "Quantum Nondemolition Monitoring of Universal Quantum Computers" Physical Review Letters. 80・3. 631-634 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] J.Shinoda: "Strong polynomial-time reducibility" Annals of Pure and Applied Logic. 84. 97-117 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] D.Burke: "Ideals and combinatorial principles" Journal of Symbolic Logic. 62・1. 117-122 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Morimoto: "Evolutionary Game Theory with Mntations for Finite Populations" Studies in Informatics and sciences. 5. 117-130 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Masanao Ozawa: "Phase Operator Problem and Macroscopic Extemsiom of Quatuam Mechanics" Annals of Physics.

    • Related Report
      1996 Annual Research Report
  • [Publications] Masanao Ozawa: "Tncompleteness of the Hyperreals:An appli cation of Forcing to Ninstandard Analysis" Proc.5th Annual of the International Workshop in Analysis and Its Applications.

    • Related Report
      1996 Annual Research Report
  • [Publications] Masanao Ozawa: "Quantum State Reduction and the Quantum Bayes Principle" Quantum Communicatim,Comruting and Measurement C Plenum,Ed O.HiRota et al.

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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