Crystallography Reports

, Volume 48, Issue 6, pp 899–913 | Cite as

To the 150th anniversary of the birth of Evgraf Stepanovich Fedorov (1853–1919) Irregularities in the fate of the theory of regularity

  • R. V. Galiulin
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. V. Fedorova, Our Workdays, Sorrows, and Joys. Memoirs Scientific Heritage (Nauka, Moscow, 1992), Vol. 20.Google Scholar
  2. 2.
    E. S. Fedorov, The Symmetry of Real Systems of Configurations. Imperial Petersburg Academy of Sciences. Scientific Heritage (Nauka, Moscow, 1991), Vol. 16, p. 168.Google Scholar
  3. 3.
    E. S. Fedorov, The Elements of the Study of Configurations. Transactions of the St. Petersburg Mineralogical Society (1885), Part 21.Google Scholar
  4. 4.
    A. V. Gadolin, Derivation of All Crystallographic Systems and Their Subsystems from One Common Origin (Akad. Nauk SSSR, Moscow, 1954).Google Scholar
  5. 5.
    R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, Mass., 1966; Mir, Moscow, 1977), Vol. 7.Google Scholar
  6. 6.
    R. V. Galiulin, Priroda (Moscow), No. 12, 20 (1991).Google Scholar
  7. 7.
    I. M. Smirnova and V. A. Smirnov, Geometry. Handbook for the 7–9 Grades of Primary Schools (Prosveshchenie, Moscow, 2001).Google Scholar
  8. 8.
    B. N. Delone, Izv. Akad. Nauk SSSR, Ser. Mat., No. 23, 365 (1959).Google Scholar
  9. 9.
    A. V. Shubnikov, Izv. Imp. Akad. Nauk, Ser. 6 10(9), 757 (1916).Google Scholar
  10. 10.
    R. V. Galiulin, Kvant, No. 11, 10 (1983).Google Scholar
  11. 11.
    I. M. Smirnova, In the World of Polyhedra (Prosveshchenie, Moscow, 1995).Google Scholar
  12. 12.
    I. M. Smirnova, Geometry (Prosveshchenie, Moscow, 1997).Google Scholar
  13. 13.
    A. N. Golovanova and R. V. Galiulin, in Proceedings of International Conference on Mineralogy and Life (Syk-tyvkar, 2000), p. 172.Google Scholar
  14. 14.
    B. N. Delone, Tr. Inst. Istor. Estestvozn. Tekh. Akad. Nauk SSSR 10, 5 (1956).MATHGoogle Scholar
  15. 15.
    P. N. Antonyuk, in Proceedings of VII All-Russian School on Modern Problems of Gas Dynamics (Moscow, 1991), p. 87.Google Scholar
  16. 16.
    M. Sh. Yakupov, in Proceedings of International Conference on Geometrization of Physics (Kazan, 1992), p. 1.Google Scholar
  17. 17.
    B. Delone and O. Zhitomirskii, Book on Geometrical Problems (GITTL, Moscow, 1952).Google Scholar
  18. 18.
    I. Kh. Sabitov, Priroda (Moscow), No. 4, 19 (2000).Google Scholar
  19. 19.
    E. S. Fedorov, Zh. Russ. Fiz.-Khim. O-va 13(4), 244 (1881).Google Scholar
  20. 20.
    S. A. Shchukarev and R. B. Dobrotin, Crystallography (Leningr. Gorn. Inst., Leningrad, 1955), No. 3, p. 81.Google Scholar
  21. 21.
    E. S. Fedorov, Crystallography (Leningr. Gorn. Inst., Leningrad, 1955), No. 3, p. 85.Google Scholar
  22. 22.
    R. V. Galiulin, Zh. Vychisl. Mat. Mat. Fiz. 43(6), 791 (2003).MathSciNetGoogle Scholar
  23. 23.
    T. F. Veremeichik and R. V. Galiulin, in Proceedings of International Conference on Crystal Genesis and Mineralogy (St. Petersburg, 2001), p. 409.Google Scholar
  24. 24.
    R. V. Galiulin, in Proceedings of International Conference on Carbon, Syktyvkar, 2003 (in press).Google Scholar
  25. 25.
    A. E. Fersman, Nauka Rabot. (Petersburg), No. 1, 13 (1920).Google Scholar
  26. 26.
    A. E. Fersman, Tr. Inst. im. M.V. Lomonosova, Ser. Obshch., No. 1, 39 (1932).Google Scholar
  27. 27.
    T. F. Veremeichik and R. V. Galiulin, Neorg. Mater. 38(9), 1110 (2002).Google Scholar
  28. 28.
    A. A. Marakushev, Periodic System of Extremum States of Chemical Elements (Nauka, Moscow, 1987).Google Scholar
  29. 29.
    R. V. Galiulin, in Proceedings of 2nd International Conference on Carbon: Fundamental Problems of Science, Materials Science, Technology (Mosk. Gos. Univ., Moscow, 2003).Google Scholar
  30. 30.
    R. V. Galiulin, Vestn. Nizhegorod. Univ. im. N.I. Lobachevskogo, Fiz. Tverd. Tela, No. 1 (4), 152 (2001).Google Scholar
  31. 31.
    E. S. Fedorov, Zap. Imp. S.-Peterb. Mineral. O-va, No. 28 (2), 1 (1891).Google Scholar
  32. 32.
    C. Jordan, Ann. Math. Ser. 2 2, 167 (1868/1869); Ann. Math. Ser. 2 2, 322 (1868/1869).Google Scholar
  33. 33.
    L. Sohncke, J. Reine Angew. Math. 77, 48 (1874).Google Scholar
  34. 34.
    L. Sohncke, Entwickelung Einer Theorie der Kristallstruktur (Tuebner, Leipzig, 1869).Google Scholar
  35. 35.
    A. Schönflies, Kristallsystem und Kristallstruktur (Teubner, Leipzig, 1891).Google Scholar
  36. 36.
    R. V. Galiulin and S. S. Ryshkov, Problems in Crystallology (Mosk. Gos. Univ., Moscow, 1971), p. 290.Google Scholar
  37. 37.
    E. S. Fedorov, Abh. K. Bauer Akad. Wiss. 11, 465 (1899).Google Scholar
  38. 38.
    B. N. Delone, Science and Mankind (Znanie, Moscow, 1981), p. 160.Google Scholar
  39. 39.
    R. V. Galiulin, Kristallografiya 29(4), 638 (1984) [Sov. Phys. Crystallogr. 29, 378 (1984)].MathSciNetGoogle Scholar
  40. 40.
    B. K. Vainshtein and R. V. Galiulin, in Physical Encyclopedia (1988), Vol. 1, p. 226.Google Scholar
  41. 41.
    D. K. Faddeev, Tables of the Main Unitary Representations of the Fedorov Groups (Akad. Nauk SSSR, Moscow, 1961; Pergamon Press, Oxford, 1964).Google Scholar
  42. 42.
    O. V. Kovalev, Irreducible Representations of Space Groups (Akad. Nauk Ukr. SSR, Kiev, 1961).Google Scholar
  43. 43.
    M. I. Aroyo and H. Wondratschek, Z. Kristallogr. 210, 243 (1995).MathSciNetGoogle Scholar
  44. 44.
    International Tables for X-ray Crystallography (Kynoch, Birmingham, 1952), Vol. 1.Google Scholar
  45. 45.
    International Tables for Crystallography, Vol. A: Space-Group Symmetry, Ed. by T. Hahn (Reidel, Dordrecht, 1983).Google Scholar
  46. 46.
    R. V. Galiulin, Kristallografiya 40(3), 461 (1995) [Crys-tallogr. Rep. 40, 421 (1995)].ADSMathSciNetGoogle Scholar
  47. 47.
    S. A. Bogomolov, Derivation of Regular Systems by the Fedorov Method (KUBUCh, Leningrad, 1932), Part 1; (ONTI, Leningrad, 1934), Part 2.Google Scholar
  48. 48.
    R. V. Galiulin, Kristallografiy 32(3), 769 (1987) [Sov. Phys. Crystallogr. 32, 452 (1987)].Google Scholar
  49. 49.
    H. Zassenhaus, Commun. Math. Helv. 21, 117 (1948).MATHMathSciNetGoogle Scholar
  50. 50.
    H. Brown, R. Bulow, J. Neubusser, H. Wondratschek, and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space (Wiley, New York, 1978).Google Scholar
  51. 51.
    R. V. Galiulin, Matrix-Vector Method of Deviation of the Fedorov Group, Available from VINITI, Moscow, No. 1094-69.Google Scholar
  52. 52.
    R. V. Galiulin and B. N. Delone, Dokl. Akad. Nauk SSSR 210(1), 85 (1973) [Sov. Phys. Dokl. 18, 285 (1973)].MathSciNetGoogle Scholar
  53. 53.
    V. I. Vernadsky, Selected Works. Crystallography (Nauka, Moscow, 1988), p. 66.Google Scholar
  54. 54.
    Y. V. Wulff, Z. Kristallogr. 45, 433 (1908).Google Scholar
  55. 55.
    A. A. Vlasov, Vestn. Mosk. Univ., Nos. 3–4, 63 (1946).Google Scholar
  56. 56.
    L. S. Kuz’menkov, Prosesses of Real Crystal Formation (Nauka, Moscow, 1977), p. 221.Google Scholar
  57. 57.
    D. D. Ivanenko and R. V. Galiulin, in Proceedings of 17th Workshop Dedicated to the 140th Birth Anniversary of Henri Poincare, Protvino, 1995, p. 180.Google Scholar
  58. 58.
    G. B. Bokii, Problems of Crystallology (GEOS, Moscow, 1999), p. 31.Google Scholar
  59. 59.
    N. V. Belov, Structural Crystallography (Akad. Nauk SSSR, Moscow, 1951).Google Scholar
  60. 60.
    G. M. Popov and I. I. Shafranovskii, Crystallography (Vysshaya Shkola, Moscow, 1972).Google Scholar
  61. 61.
    Yu. G. Zagal’skaya, G. P. Litvinskaya, R. V. Galiulin, and V. S. Kovalenko, Problems of Crystallology (Mosk. Gos. Univ., Moscow, 1971), p. 284.Google Scholar
  62. 62.
    M. P. Shaskol’skaya, Crystallography (Vysshaya Shkola, Moscow, 1984).Google Scholar
  63. 63.
    E. S. Fedorov, Zap. Imper. S.-Peterb. Mineral. O-va, No. 28 (2), 345 (1891).Google Scholar
  64. 64.
    N. V. Belov, Kristallografiya 1(5), 612 (1956) [Sov. Phys. Crystallogr. 1, 482 (1956)].Google Scholar
  65. 65.
    Kh. S. Mamedov, Comput. Math. Appl. 128, 511 (1986).Google Scholar
  66. 66.
    E. S. Fedorov, Izv. S.-Peterb. Biol. Lab. 8(1), 25 (1906); Izv. S.-Peterb. Biol. Lab. 8 (2), 9 (1906).Google Scholar
  67. 67.
    M. D. Frank-Kamenetskii, The Most Important Molecule (Nauka, Moscow, 1983).Google Scholar
  68. 68.
    A. L. Mackay, Kristallografiya 26(5), 910 (1981) [Sov. Phys. Crystallogr. 26, 517 (1981)].MathSciNetGoogle Scholar
  69. 69.
    J. D. Bernal and S. H. Carlise, Kristallografiya 13(5), 927 (1968) [Sov. Phys. Crystallogr. 13, 811 (1968)].Google Scholar
  70. 70.
    R. V. Galiulin, Usp. Fiz. Nauk 172, 229 (2002).Google Scholar
  71. 71.
    R. V. Galiulin, in Proceedings of Scientific Seminar on Nontraditional Problems of Geology (Moscow, 2002), p. 52.Google Scholar
  72. 72.
    O. V. Konovalov and R. V. Galiulin, Kristallografiya 34(3), 731 (1989) [Sov. Phys. Crystallogr. 34, 435 (1989)].MathSciNetGoogle Scholar
  73. 73.
    E. S. Fedorov, Zap. S.-Peterb. Mineral. O-va, Ser. 2, No. 17, 381 (1882).Google Scholar
  74. 74.
    K. Dornberger-Schiff, Lehrgang über OD-Strukturen (Akademie, Berlin, 1966; Mosk. Gos. Univ., Moscow, 1966).Google Scholar
  75. 75.
    R. V. Galiulin, Kristallografiya 43(2), 366 (1998) [Crys-tallogr. Rep. 43, 332 (1998)].Google Scholar
  76. 76.
    D. Gratia, Usp. Fiz. Nauk 156(2), 347 (1988).Google Scholar
  77. 77.
    V. M. Vil’chek, Algorithms of History (Prometei, Moscow, 1989).Google Scholar
  78. 78.
    E. S. Fedorov, The Realm of Crystals. Tables for Crystallochemical Analysis (Zap. Akad. Nauk Fiz.-Mat. Otd., 1920), Vol. 36.Google Scholar
  79. 79.
    V. I. Arnol’d, Izv. Ross. Akad. Nauk, Ser. Yaz. Lit. 56(2), 63 (1997).Google Scholar
  80. 80.
    V. I. Arnol’d, Usp. Fiz. Nauk 169(12), 1311 (1999) [Phys. Usp. 42, 1205 (1999)].Google Scholar
  81. 81.
    L. D. Faddeev, Chto Novogo Nauke Tekh., No. 2 (4), 112 (2003).Google Scholar
  82. 82.
    S. Singh, Fermat’s Enigma: the Epic Quest to Solve the World’s Greatest Mathematical Problem (Anchor Books, New York, 1998; Mosk. Tsentr Neprer. Mat. Obraz., Moscow, 2000).Google Scholar
  83. 83.
    I. A. Sheremet’ev, Kristallografiya 46(2), 199 (2001) [Crystallogr. Rep. 46, 161 (2001)].Google Scholar
  84. 84.
    V. V. Nikulin and I. R. Shafarevich, Geometries and Groups (Nauka, Moscow, 1983).Google Scholar
  85. 85.
    S. V. Rudnev, Comput. Math. Appl. 16(5–8), 597 (1988).MATHMathSciNetGoogle Scholar
  86. 86.
    R. V. Galiulin, Sci. Spectra 14, 54 (1998).Google Scholar
  87. 87.
    R. V. Galiulin, Usp. Fiz. Nauk 172(2), 229 (2002).Google Scholar
  88. 88.
    R. V. Galiulin and T. F. Veremeichik, in Proceedings of International Conference Dedicated to M.P. Shaskol’skaya, Moscow, 2003 (in press).Google Scholar
  89. 89.
    E. S. Fedorov, Zap. S.-Peterb. Mineral. O-va, Ser. 2, No. 30, 455 (1893).Google Scholar
  90. 90.
    V. I. Arnol’d, What is Mathematics? (Mosk. Tsentr Neprer. Mat. Obraz., Moscow, 2002).Google Scholar
  91. 91.
    E. S. Fedorov, Fundamentals of Differential and Integral Calculus (Imper. Akad. Nauk, St. Petersburg, 1903).Google Scholar
  92. 92.
    E. S. Fedorov, Fundamentals of Differential and Integral Calculus, Drawings (Imper. Akad. Nauk, St. Petersburg, 1903).Google Scholar
  93. 93.
    E. S. Fedorov, Scientific Heritage (Nauka, Leningrad, 1991), Vol. 16.Google Scholar
  94. 94.
    I. I. Shafranovskii, Crystallography in the USSR, 1917–1991 (Nauka, St. Petersburg, 1996).Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2003

Authors and Affiliations

  • R. V. Galiulin
    • 1
  1. 1.Shubnikov Institute of CrystallographyRussian Academy of SciencesMoscowRussia

Personalised recommendations