Elements of Iso-, Geno-, Hyper-Mathematics for Matter, Their Isoduals for Antimatter, and Their Applications in Physics, Chemistry, and Biology

Abstract

Pre-existing mathematical formulations are generally used for the treatment of new scientific problems. In this note we show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter. These novel mathematics are based on the lifting of the multiplicative unit of ordinary fields (with characteristic zero) from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathematics; (2) invertible, non-Hermitean, and single-valued units for genomathematics; and (3) invertible, non-Hermitean, and multi-valued units for hypermathematics; with corresponding liftings of the conventional associative product and consequential lifting of all branches of mathematics admitting a (left and right) multiplicative unit. An anti-Hermitean conjugation applied to the totality of quantities and their operation of the preceding mathematics characterizes the isodual mathematics. Intriguingly, the emerging formulations preserve the abstract axioms of conventional mathematics (that based on the unit +1). As such, the new formulations result to be new realizations of existing abstract mathematical axioms. We then show that the above mathematical advances permit corresponding liftings of conventional classical and quantum theories with a resolution of basic open problems in physics, chemistry, and biology, numerous experimental verifications, as well as new industrial applications.

This is a preview of subscription content, log in to check access.

REFERENCES

  1. 1.

    I. Newton, Philosophiae Naturalis Principia Mathematica (1687), translated and reprinted by Cambridge University Press (1934).

  2. 2.

    J. L. Lagrange, Mechanique Analytique (1788), reprinted by Gauthier-Villars, Paris (1888).

  3. 3.

    W. R. Hamilton, On a General Method in Dynamics (1834), reprinted in Hamilton's Collected Works (Cambridge University Press, 1940).

  4. 4.

    S. Lie, Over en Classe Geometriske Transformationer, English translation by E. Trell, Algebras Groups and Geometries 15, 395(1998).

    Google Scholar 

  5. 5.

    A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777(1935).

    Google Scholar 

  6. 6.

    P. A. M. Dirac, The Principles of Quantum Mechanics, 4th edn. (Clarendon Press, Oxford, 1958).

    Google Scholar 

  7. 7.

    A. A. Albert, Trans. Amer. Math. Soc. 64, 552(1948).

    Google Scholar 

  8. 8.

    R. M. Santilli, Nuovo Cimento 51, 570(1967).

    Google Scholar 

  9. 9.

    R. M. Santilli, Suppl. Nuovo Cimento 6, 1225(1968).

    Google Scholar 

  10. 10.

    R. M. Santilli, Hadronic J. 3, 440(1979).

    Google Scholar 

  11. 11.

    R. M. Santilli, Hadronic J. 8, 25and 36 (1985).

    Google Scholar 

  12. 12.

    R. M. Santilli, Algebras, Groups, and Geometries 10, 273(1993).

    Google Scholar 

  13. 13.

    R. M. Santilli and T. Vougiouklis, contributed paper in New Frontiers in Hyperstructures, T. Vougiouklis, ed. (Hadronic Press, 1996), p. 1.

  14. 14.

    R. M. Santilli, Rendiconti Circolo Matematico di Palermo, Supplemento 42, 7(1996).

    Google Scholar 

  15. 15.

    R. M. Santilli, Intern. J. Mod. Phys. D 7, 351(1998).

    Google Scholar 

  16. 16.

    R. M. Santilli, Comm. Theor. Phys. 3, 153(1993).

    Google Scholar 

  17. 17.

    R. M. Santilli, Hadronic J. 17, 257(1994).

    Google Scholar 

  18. 18.

    R. M. Santilli, Hadronic J. 17, 285(1994).

    Google Scholar 

  19. 19.

    R. M. Santilli, Communications of the JINR (Dubna, Russia, 1996), No. E2–96–259.

    Google Scholar 

  20. 20.

    R. M. Santilli, contributed paper in New Frontiers of Hadronic Mechanics, T. L. Gill, ed. (Hadronic Press, 1996).

  21. 21.

    R. M. Santilli, Hyperfine Interactions 109, 63(1997).

    Google Scholar 

  22. 22.

    R. M. Santilli, Intern. J. Mod. Phys. A 14, 2205(1999).

    Google Scholar 

  23. 23.

    R. M. Santilli, Hadronic J. 1, 224(1978).

    Google Scholar 

  24. 24.

    R. M. Santilli, Phys. Rev. D 20, 555(1979).

    Google Scholar 

  25. 25.

    C. Myung and R. M. Santilli, Hadronic J. 5, 1277(1982).

    Google Scholar 

  26. 26.

    R. M. Santilli, Nuovo Cimento Lett. 37, 545(1983).

    Google Scholar 

  27. 27.

    R. M. Santilli, Hadronic J. 8, 25and 36 (1985).

    Google Scholar 

  28. 28.

    R. M. Santilli, JINR Rapid Comm. 6, 24(1993).

    Google Scholar 

  29. 29.

    R. M. Santilli, J. Moscow Phys. Soc. 3, 255(1993).

    Google Scholar 

  30. 30.

    R. M. Santilli, Chinese J. Syst. Ing. & Electr. 6, 177(1996).

    Google Scholar 

  31. 31.

    R. M. Santilli, Found. Phys. 27, 635(1997).

    Google Scholar 

  32. 32.

    R. M. Santilli, Found. Phys. Lett. 10, 307(1997).

    Google Scholar 

  33. 33.

    R. M. Santilli, Acta Appl. Math. 50, 177(1998).

    Google Scholar 

  34. 34.

    R. M. Santilli, contributed paper to the Proceedings of the International Workshop on Modern Modified Theories of Gravitation and Cosmology, E. I. Guendelman, ed. (Hadronic Press, 1998), p. 113.

  35. 35.

    R. M. Santilli, contributed paper to the Proceedings of the VIII M. Grossmann Meeting on General Relativity, Jerusalem, June 1998 (World Scientific, 1999), p. 473.

  36. 36.

    R. M. Santilli, contributed paper in Photons: Old Problems in Light of New Ideas, V. V. Dvoeglazov, ed. (Nova Science Publishers, 2000), pp. 421–442.

  37. 37.

    R. M. Santilli, Found. Phys. Lett. 32, 1111(2002).

    Google Scholar 

  38. 38.

    R. M. Santilli, Hadronic J. 1, 574and 1267 (1978).

    Google Scholar 

  39. 39.

    R. M. Santilli, Hadronic J. 2, 1460(1979) and R. M. Santilli, Hadronic J. 3, 914 (1980).

    Google Scholar 

  40. 40.

    R. M. Santilli, Hadronic J. 4, 1166(1981).

    Google Scholar 

  41. 41.

    R. M. Santilli, Hadronic J. 5, 264(1982).

    Google Scholar 

  42. 42.

    H. C. Myung and R. M. Santilli, Hadronic J. 5, 1367(1982).

    Google Scholar 

  43. 43.

    R. M. Santilli, Hadronic J. Suppl. 1, 662(1985).

    Google Scholar 

  44. 44.

    R. M. Santilli, Found. Phys. 27, 1159(1997).

    Google Scholar 

  45. 45.

    R. M. Santilli, Mod. Phys. Lett. 13, 327(1998).

    Google Scholar 

  46. 46.

    R. M. Santilli, Intern. J. Mod. Phys. A 14, 3157(1999).

    Google Scholar 

  47. 47.

    R. M. Santilli, Algebras, Groups, and Geometries 15, 473(1998).

    Google Scholar 

  48. 48.

    R. M. Santilli, Foundations of Theoretical Mechanics, Vol. I (Springer, Heidelberg/New York, 1978).

    Google Scholar 

  49. 49.

    R. M. Santilli, Lie-Admissible Approach to the Hadronic Structure, Vol. I (Hadronic Press, Palm Harbor, Florida, 1978).

    Google Scholar 

  50. 50.

    R. M. Santilli, Lie-Admissible Approach to the Hadronic Structure, Vol. II (Hadronic Press, Palm Harbor, Florida, 1981).

    Google Scholar 

  51. 51.

    R. M. Santilli, Foundations of Theoretical Mechanics, Vol. II (Springer, Heidelberg/New York, 1983).

    Google Scholar 

  52. 52.

    R. M. Santilli, Isotopic Generalizations of Galilei and Einstein Relativities, Vol. I (Hadronic Press, Palm Harbor, Florida, 1991).

    Google Scholar 

  53. 53.

    R. M. Santilli, Isotopic Generalizations of Galilei and Einstein Relativities, Vol. II (Hadronic Press, Palm Harbor, Florida, 1991).

    Google Scholar 

  54. 54.

    R. M. Santilli, Elements of Hadronic Mechanics, Vol. I, 2nd Edn. (Ukraine Academy of Sciences, Kiev, 1995).

    Google Scholar 

  55. 55.

    R. M. Santilli, Elements of Hadronic Mechanics, Vol. II, 2nd Edn. (Ukraine Academy of Sciences, Kiev, 1995).

    Google Scholar 

  56. 56.

    C. R. Illert and R. M. Santilli, Foundations of Theoretical Conchology (Hadronic Press, Palm Harbor, Florida, 1995).

    Google Scholar 

  57. 57.

    R. M. Santilli, Isotopic, Genotopic, and Hyperstructural Methods in Theoretical Biology (Ukraine Academy of Sciences, Kiev, 1996).

    Google Scholar 

  58. 58.

    R. M. Santilli, The Physics of New Clean Energies and Fuels According to Hadronic Mechanics, Special issue of the Journal of New Energy, 318 pages (1998), and http://www.neutronstructure.org

  59. 59.

    R. M. Santilli, Foundations of Hadronic Chemistry with Applications to New Clean Energies and Fuels (Kluwer Academic, Boston, Dordrecht, London, 2001), and http://www.magnegas.com

    Google Scholar 

  60. 60.

    R. M. Santilli, Isodual Theory of Antimatter, with Applications to Cosmology, Antigravity and Spacetime Machines, in preparation.

  61. 61.

    R. M. Santilli, Elements of Hadronic Mechanics, Vol. III, in preparation.

  62. 62.

    H. C. Myung, Lie Algebras and Flexible Lie-Admissible Algebras (Hadronic Press, 1982).

  63. 63.

    A. K. Aringazin, A. Jannussis, D. F. Lopez, M. Nishioka, and B. Veljanoski, Santilli's Lie-Isotopic Generalization of Galilei's and Einstein's Relativities (Kostarakis Publishers, Athens, 1991).

    Google Scholar 

  64. 64.

    D. S. Sourlas and G. T. Tsagas, Mathematical Foundations of the Lie–Santilli Theory (Ukraine Academy of Sciences, Kiev, 1993).

    Google Scholar 

  65. 65.

    J. Lôhmus, E. Paal, and L. Sorgsepp, Nonassociative Algebras in Physics (Hadronic Press, Palm Harbor, Florida, 1994).

    Google Scholar 

  66. 66.

    J. V. Kadeisvili, Santilli's Isotopies of Contemporary Algebras, Geometries, and Relativities, 2nd Edn. (Ukraine Academy of Sciences, Kiev, 1997).

    Google Scholar 

  67. 67.

    R. M. Falcon Ganfornina and J. Nunez Valdes, Fondamentos de la Isoteoria de Lie–Santilli, in Spanish (International Academic Press, America-Europe-Asia, 2001), also available in the pdf file http://www.i-b-r.org/docs/spanish.pdf.

    Google Scholar 

  68. 68.

    Chun-Xuan Jiang, Foundations of Santilli's Isonumber Theory, with Applications to New Cryptograms, Fermat's Theorem, and Goldbach's Conjecture (International Academic Press, America-Europe-Asia, 2002), also available in the pdf file http://www.i-b-r.org/docs/jiang.pdf.

    Google Scholar 

  69. 69.

    H. C. Myung and S. Okubo, eds., Applications of Lie-Admissible Algebras in Physics, Vol. I (Hadronic Press, 1978).

  70. 70.

    H. C. Myung and S. Okubo, Editors, Applications of Lie-Admissible Algebras in Physics, Vol. II (Hadronic Press, 1978).

  71. 71.

    H. C. Myung and R. M. Santilli, ed., “Proceedings of the second workshop on Lie-admissible formulations, Part I, ” Hadronic J. 2(6), 1252–2033 (1979).

  72. 72.

    H. C. Myung and R. M. Santilli, ed., “Proceedings of the second workshop on Lie-admissible formulations, Part II, ” Hadronic J. 3(1), 1–725 (1980).

    Google Scholar 

  73. 73.

    H. C. Myung and R. M. Santilli, ed., “Proceedings of the third workshop on Lie-admissible formulations, Part A, ” Hadronic J. 4(2), 183–607 (1981).

  74. 74.

    H. C. Myung and R. M. Santilli, ed., “Proceedings of the third workshop on Lie-admissible formulations, Part B, ” Hadronic J. 4(3), 608–1165 (1981).

    Google Scholar 

  75. 75.

    H. C. Myung and R. M. Santilli, ed., “Proceedings of the third workshop on Lie-admissible formulations, Part C, ” Hadronic J. 4(4), 1166–1625 (1981).

  76. 76.

    J. Fronteau, A. Tellez-Arenas, and R. M. Santilli, ed., “Proceedings of the first international conference on nonpotential interactions and their Lie-admissible treatment, Part A, ” Hadronic J. 5(2), 245–678 (1982).

  77. 77.

    J. Fronteau, A. Tellez-Arenas, and R. M. Santilli, ed., “Proceedings of the first international conference on nonpotential interactions and their Lie-admissible treatment, Part B, ” Hadronic J. 5(3), 679–1193 (1982).

  78. 78.

    J. Fronteau, A. Tellez-Arenas, and R. M. Santilli, ed., “Proceedings of the first international conference on nonpotential interactions and their Lie-admissible treatment, Part C, ” Hadronic J. 5(4), 1194–1626 (1982).

  79. 79.

    J. Fronteau, A. Tellez-Arenas, and R. M. Santilli, ed., “Proceedings of the first international conference on nonpotential interactions and their Lie-admissible treatment, Part D, ” Hadronic J. 5(5), 1627–1948 (1982).

  80. 80.

    J. Fronteau, R. Mignani, H. C. Myung, and R. M. Santilli, eds., “Proceedings of the first workshop on hadronic mechanics, ” Hadronic J. 6(6), 1400–1989 (1983).

  81. 81.

    A. Shoeber, ed., Irreversibility and Nonpotentiality in Statistical Mechanics (Hadronic Press, 1984).

  82. 82.

    H. C. Myung, ed., Mathematical Studies in Lie-Admissible Algebras, Vol. I (Hadronic Press, 1984).

  83. 83.

    H. C. Myung, ed., Mathematical Studies in Lie-Admissible Algebras, Vol. II (Hadronic Press, 1984).

  84. 84.

    H. C. Myung and R. M. Santilli, ed., Applications of Lie-Admissible Algebras in Physics, Vol. III (Hadronic Press, 1984).

  85. 85.

    J. Fronteau, R. Mignani, and H. C. Myung, eds., “Proceedings of the second workshop on hadronic mechanics, ” Vol. I, Hadronic J. 7(5), 911–1258 (1984).

  86. 86.

    J. Fronteau, R. Mignani, and H. C. Myung, eds., “Proceedings of the second workshop on hadronic mechanics, ” Vol. II, Hadronic J. 7(6), 1259–1759 (1984).

  87. 87.

    D. M. Norris et al., Tomber's Bibliography and Index in Nonassociative Algebras (Hadronic Press, Palm Harbor, Florida, 1984).

    Google Scholar 

  88. 88.

    H. C. Myung, ed., Mathematical Studies in Lie-Admissible Algebras, Vol. III (Hadronic Press, 1986).

  89. 89.

    A. D. Jannussis, R. Mignani, M. Mijatovic, H. C. Myung, B. Popov, and A. Tellez Arenas, eds., Fourth Workshop on Hadronic Mechanics and Nonpotential Interactions (Nova Science, New York, 1990).

    Google Scholar 

  90. 90.

    H. M. Srivastava and Th. M. Rassias, eds., Analysis Geometry and Groups: A Riemann Legacy Volume (Hadronic Press, 1993).

  91. 91.

    F. Selleri, ed., Fundamental Questions in Quantum Physics and Relativity (Hadronic Press, 1993).

  92. 92.

    J. V. Kadeisvili, ed., The Mathematical Legacy of Hanno Rund (Hadronic Press, 1994).

  93. 93.

    M. Barone and F. Selleri, eds., Frontiers of Fundamental Physics (Plenum, New York, 1994).

    Google Scholar 

  94. 94.

    M. Barone and F. Selleri, eds., Advances in Fundamental Physics (Hadronic Press, 1995).

  95. 95.

    Gr. Tsagas, ed., New Frontiers in Algebras, Groups, and Geometries (Hadronic Press, 1996).

  96. 96.

    T. Vougiouklis, ed., New Frontiers in Hyperstructures (Hadronic Press, 1996).

  97. 97.

    T. L. Gill, ed., New Frontiers in Hadronic Mechanics (Hadronic Press, 1996).

  98. 98.

    T. L. Gill, ed., New Frontiers in Relativities (Hadronic Press, 1996).

  99. 99.

    T. L. Gill, ed., New Frontiers in Physics, Vol. I (Hadronic Press, 1996).

  100. 100.

    T. L. Gill, ed., New Frontiers in Physics, Vol. II (Hadronic Press, 1996).

  101. 101.

    C. A. Dreismann, ed., New Frontiers in Theoretical Biology (Hadronic Press, 1996).

  102. 102.

    G. A. Sardanashvily, ed., New Frontiers in Gravitation (Hadronic Press, 1996).

  103. 103.

    M. Holzscheiter, ed., Proceedings of the International Workshop on Antimatter Gravity, Sepino, Molise, Italy, May 1996, Hyperfine Interactions, Vol. 109 (1997).

  104. 104.

    T. Gill, K. Liu, and E. Trell, eds., Fundamental Open Problems in Science at the End of the Millennium, Vol. I (Hadronic Press, 1999).

  105. 105.

    T. Gill, K. Liu, and E. Trell, eds., Fundamental Open Problems in Science at the End of the Millennium, Vol. II (Hadronic Press, 1999).

  106. 106.

    T. Gill, K. Liu, and E. Trell, eds., Fundamental Open Problems in Science at the End of the Millennium, Vol. III (Hadronic Press, 1999).

  107. 107.

    V. V. Dvoeglazov, ed., Photon: Old Problems in Light of New Ideas (Nova Science, 2000).

  108. 108.

    M. C. Duffy and M. Wegener, eds., Recent Advances in Relativity Theory, Vol. I (Hadronic Press, 2000).

  109. 109.

    M. C. Duffy and M. Wegener, eds., Recent Advances in Relativity Theory, Vol. I (Hadronic Press, 2000).

  110. 110.

    F. Cardone, R. Mignani, and R. M. Santilli, J. Phys. G: Nucl. Part. Phys. 18, L61(1992).

    Google Scholar 

  111. 111.

    F. Cardone, R. Mignani, and R. M. Santilli, J. Phys. G: Nucl. Part. Phys. 18, L141(1992).

    Google Scholar 

  112. 112.

    R. M. Santilli, Hadronic J. 15, Part I: 1–501992 and R. M. Santilli, Hadronic J. 15 Part II: 77134 (1992).

    Google Scholar 

  113. 113.

    Cardone and R. Mignani, JETP 88, 435(1995).

    Google Scholar 

  114. 114.

    R. M. Santilli, Intern. J. of Phys. 4, 1(1998).

    Google Scholar 

  115. 115.

    R. M. Santilli, Commun. Math. Theor. Phys. 2, 1(1999).

    Google Scholar 

  116. 116.

    A. O. E. Animalu and R. M. Santilli, Intern. J. Quantum Chem. 26, 175(1995).

    Google Scholar 

  117. 117.

    R. M. Santilli, contributed paper to Frontiers of Fundamental Physics, M. Barone and F. Selleri, eds. (Plenum, New York, 1994), pp. 4158.

    Google Scholar 

  118. 118.

    R. Mignani, Physics Essays 5, 531(1992).

    Google Scholar 

  119. 119.

    R. M. Santilli, Comm. Theor. Phys. 4, 123(1995).

    Google Scholar 

  120. 120.

    Yu. Arestov, V. Solovianov, and R. M. Santilli, Found. Phys. Lett. 11, 483(1998).

    Google Scholar 

  121. 121.

    R. M. Santilli, contributed paper in the Proceedings of the International Symposium on Large Scale Collective Motion of Atomic Nuclei, G. Giardina, G. Fazio, and M. Lattuada, eds. (World Scientific, Singapore, 1997), p. 549.

    Google Scholar 

  122. 122.

    J. Ellis, N. E. Mavromatos, and D. V. Napoulos, in Proceedings of the Erice Summer School, 31st Course: From Superstrings to the Origin of Space-Time (World Sientific, 1996).

  123. 123.

    Borghi, C. Giori, and A. Dall'OIlio, Russian J. Nucl. Phys. 56, 147(1993).

    Google Scholar 

  124. 124.

    N. F. Tsagas, A. Mystakidis, G. Bakos, and L. Seftelis, Hadronic J. 19, 87(1996).

    Google Scholar 

  125. 125.

    R. M. Santilli and D. D. Shillady, Intern. J. Hydrogen Energy 24, 943(1999).

    Google Scholar 

  126. 126.

    R. M. Santilli and D. D. Shillady, Intern. J. Hydrogen Energy 25, 173(2000).

    Google Scholar 

  127. 127.

    R. M. Santilli, Hadronic J. 21, 789–894 (1998).

    Google Scholar 

  128. 128.

    M. G. Kucherenko and A. K. Aringazin, Hadronic J. 21, 895(1998).

    Google Scholar 

  129. 129.

    M. G. Kucherenko and A. K. Aringazin, Hadronic J. 23, 59(2000).

    Google Scholar 

  130. 130.

    R. M. Santilli and A. K. Aringazin, “Structure and combustion of magnegases, ” e-;print http://arxiv.org/abs/physics/0112066, to be published.

  131. 131.

    S. Okubo, Hadronic J. 5, 1564(1982).

    Google Scholar 

  132. 132.

    J. V. Kadeisvili, Algebras, Groups, and Geometries 9, 283and 319 (1992).

    Google Scholar 

  133. 133.

    J. V. Kadeisvili, N. Kamiya, and R. M. Santilli, Hadronic J. 16, 168(1993).

    Google Scholar 

  134. 134.

    J. V. Kadeisvili, Algebras, Groups, and Geometries 9, 283(1992).

    Google Scholar 

  135. 135.

    J. V. Kadeisvili, Algebras, Groups, and Geometries 9, 319(1992).

    Google Scholar 

  136. 136.

    J. V. Kadeisvili, contributed paper in the Proceedings of the International Workshop on Symmetry Methods in Physics, G. Pogosyan et al., eds. (JINR, Dubna, Russia, 1994).

    Google Scholar 

  137. 137.

    J. V. Kadeisvili, Math. Methods in Appl. Sci. 19, 1349(1996).

    Google Scholar 

  138. 138.

    J. V. Kadeisvili, Algebras, Groups, and Geometries 15, 497(1998).

    Google Scholar 

  139. 139.

    G. T. Tsagas and D. S. Sourlas, Algebras, Groups, and Geometries 12, 1(1995).

    Google Scholar 

  140. 140.

    G. T. Tsagas and D. S. Sourlas, Algebras, Groups, and Geometries 12, 67(1995).

    Google Scholar 

  141. 141.

    G. T. Tsagas, Algebras, Groups, and Geometries 13, 129(1996).

    Google Scholar 

  142. 142.

    G. T. Tsagas, Algebras, Groups, and Geometries 13, 149(1996).

    Google Scholar 

  143. 143.

    E. Trell, “Isotopic proof and reproof of Fermat's last theorem verifying Beal's conjecture, ” Algebras, Groups, and Geometries 15, 299–318 (1998).

    Google Scholar 

  144. 144.

    A. K. Aringazin and D. A. Kirukhin, Algebras, Groups, and Geometries 12, 255(1995).

    Google Scholar 

  145. 145.

    A. K. Aringazin, A. Jannussis, D. F. Lopez, M. Nishioka, and B. Veljanoski, Algebras, Groups, and Geometries 7, 211(1990).

    Google Scholar 

  146. 146.

    A. K. Aringazin, A. Jannussis, D. F. Lopez, M. Nishioka, and B. Veljanoski, Algebras, Groups, and Geometries 8, 77(1991).

    Google Scholar 

  147. 147.

    D. L. Rapoport, Algebras, Groups, and Geometries 8, 1(1991).

    Google Scholar 

  148. 148.

    D. L. Rapoport, contributed paper in the Proceedings of the Fifth International Workshop on Hadronic Mechanics, H. C. Myung, ed. (Nova Science, 1990).

  149. 149.

    D. L. Rapoport, Algebras, Groups, and Geometries 8, 1(1991).

    Google Scholar 

  150. 150.

    C.-X. Jiang, Algebras, Groups, and Geometries 15, 509(1998).

    Google Scholar 

  151. 151.

    D. B. Lin, Hadronic J. 11, 81(1988).

    Google Scholar 

  152. 152.

    R. Aslaner and S. Keles, Algebras, Groups, and Geometries 14, 211(1997).

    Google Scholar 

  153. 153.

    R. Aslander and S. Keles, Algebras, Groups, and Geometries 15, 545(1998).

    Google Scholar 

  154. 154.

    M. R. Molaei, Algebras, Groups, and Geometries 115, 563(1998).

    Google Scholar 

  155. 155.

    S. Vacaru, Algebras, Groups, and Geometries 14, 225(1997).

    Google Scholar 

  156. 156.

    N. Kamiya and R. M. Santilli, Algebras, Groups, and Geometries 13, 283(1996).

    Google Scholar 

  157. 157.

    S. Vacaru, Algebras, Groups, and Geometries 14, 211(1997).

    Google Scholar 

  158. 158.

    Y. Ylamed, Hadronic J. 5, 1734(1982).

    Google Scholar 

  159. 159.

    R. Trostel, Hadronic J. 5, 1893(1982).

    Google Scholar 

  160. 160.

    J. P. Mills, Jr., Hadronic J. 19, 1(1996).

    Google Scholar 

  161. 161.

    J. Dunning-Davies, Found. Phys. Lett. 12, 593(1999).

    Google Scholar 

  162. 162.

    E. Trell, Hadronic J. Suppl. 12, 217(1998).

    Google Scholar 

  163. 163.

    E. Trell, Algebras, Groups, and Geometries 15, 447–471 (1998).

    Google Scholar 

  164. 164.

    E. Trell, “Tessellation of diophantine equation block universe, ” contributed paper to Physical Interpretations of Relativity Theory, September 6–9, 2002, Imperial College, London. British Society for the Philosophy of Science, in print (2002).

  165. 165.

    J. Fronteau, R. M. Santilli, and A. Tellez-Arenas, Hadronic J. 3, 130(1979).

    Google Scholar 

  166. 166.

    A. O. E. Animalu, Hadronic J. 7, 19664(1982).

    Google Scholar 

  167. 167.

    A. O. E. Animalu, Hadronic J. 9, 61(1986).

    Google Scholar 

  168. 168.

    A. O. E. Animalu, Hadronic J. 10, 321(1988).

    Google Scholar 

  169. 169.

    A. O. E. Animalu, Hadronic J. 16, 411(1993).

    Google Scholar 

  170. 170.

    A. O. E. Animalu, Hadronic J. 17, 349(1994).

    Google Scholar 

  171. 171.

    S. Okubo, Hadronic J. 5, 1667(1982).

    Google Scholar 

  172. 172.

    D. F. Lopez, in Symmetry Methods in Physics, A. N. Sissakian, G. S. Pogosyan, and X. I. Vinitsky, eds. (JINR, Dubna, Russia, 1994).

    Google Scholar 

  173. 173.

    D. F. Lopez, Hadronic J. 16, 429(1993).

    Google Scholar 

  174. 174.

    A. Jannussis and D. Skaltsas, Ann. Fond. L. de Broglie 18, 137(1993).

    Google Scholar 

  175. 175.

    A. Jannussis, R. Mignani, and R. M. Santilli, Ann. Fonnd. L. de Broglie 18, 371(1993).

    Google Scholar 

  176. 176.

    A. O. Animalu and R. M. Santilli, contributed paper in Hadronic Mechanics and Nonpotential Interactions, M. Mijatovic, ed. (Nova Science, New York, 1990), pp. 19–26.

    Google Scholar 

  177. 177.

    M. Gasperini, Hadronic J. 6, 935(1983).

    Google Scholar 

  178. 178.

    M. Gasperini, Hadronic J. 6, 1462(1983).

    Google Scholar 

  179. 179.

    R. Mignani, Hadronic J. 5, 1120(1982).

    Google Scholar 

  180. 180.

    R. Mignani, Lett. Nuovo Cimento 39, 413(1984).

    Google Scholar 

  181. 181.

    A. Jannussis, Hadronic J. Suppl. 1, 576(1985).

    Google Scholar 

  182. 182.

    A. Jannussis and R. Mignani, Physica A 152, 469(1988).

    Google Scholar 

  183. 183.

    A. Jannussis and I. Tsohantis, Hadronic J. 11, 1(1988).

    Google Scholar 

  184. 184.

    A. Jannussis, M. Miatovic, and B. Veljanosky, Physics Essays 4, (1991).

  185. 185.

    A. Jannussis, D. Brodimas, and R. Mignani, J. Phys. A: Math. Gen. 24, L775(1991).

    Google Scholar 

  186. 186.

    A. Jannussis and R. Mignani, Physica A 187, 575(1992).

    Google Scholar 

  187. 187.

    A. Jannussis, R. Mignani, and D. Skaltsas, Physica A 187, 575(1992).

    Google Scholar 

  188. 188.

    A. Jannussis et al., Nuovo Cimento B 103, 17and 537 (1989).

    Google Scholar 

  189. 189.

    A. Jannussis et al., Nuovo Cimento B 104, 33and 53 (1989).

    Google Scholar 

  190. 190.

    A. Jannussis et al., Nuovo Cimento B 108, 57(1993).

    Google Scholar 

  191. 191.

    A. Jannussis et al., Phys. Lett. A 132, 324(1988).

    Google Scholar 

  192. 192.

    A. K. Aringazin, Hadronic J. 12, 71(1989).

    Google Scholar 

  193. 193.

    A. K. Aringazin, Hadronic J. 13, 183(1990).

    Google Scholar 

  194. 194.

    A. K. Aringazin, Hadronic J. 13, 263(1990).

    Google Scholar 

  195. 195.

    A. K. Aringazin, Hadronic J. 14, 531(1991).

    Google Scholar 

  196. 196.

    A. K. Aringazin, Hadronic J. 16, 195(1993).

    Google Scholar 

  197. 197.

    A. K. Aringazin and K. M. Aringazin, invited paper, in the Proceedings of the Intern. Conference ‘Frontiers of Fundamental Physics’ (Plenum, 1993).

  198. 198.

    A. K. Aringazin, K. M. Aringazin, S. Baskoutas, G. Brodimas, A. Jannussis, and K. Vlachos, contributed paper in the Proceedings of the Intern. Conference ‘Frontiers of Fundamental Physics’ (Plenum, 1993).

  199. 199.

    A. K. Aringazin, D. A. Kirukhin, and R. M. Santilli, Hadronic J. 18, 245(1995).

    Google Scholar 

  200. 200.

    A. K. Aringazin, D. A. Kirukhin, and R. M. Santilli, Hadronic J. 18, 257(1995).

    Google Scholar 

  201. 201.

    T. L. Gill, Hadronic J. 9, 77(1986).

    Google Scholar 

  202. 202.

    T. L. Gill and J. Lindesay, Int. J. Theor. Phys. 32, 2087(1993).

    Google Scholar 

  203. 203.

    T. L. Gill, W. W. Zachary, M. F. Mahmood, and J. Lindesay, Hadronic J. 16, 28(1994).

    Google Scholar 

  204. 204.

    T. L. Gill, W. W. Zachary, and J. Lindesay, Found. Phys. Lett. 10, 547(1997).

    Google Scholar 

  205. 205.

    T. L. Gill, W. W. Zachary, and J. Lindesay, Int. J. Theor. Phys. 37, 22637(1998).

    Google Scholar 

  206. 206.

    T. L. Gill, W. W. Zachary, and J. Lindesay, Found. Phys. 31, 1299(2001).

    Google Scholar 

  207. 207.

    D. L. Schuch, K.-M. Chung, and H. Hartmann, J. Math. Phys. 24, 1652(1983).

    Google Scholar 

  208. 208.

    D. L. Schuch and K.-M. Chung, Intern. J. Quantum Chem. 19, 1561(1986).

    Google Scholar 

  209. 209.

    D. Schich, Phys. Rev. A 23, 59(1989).

    Google Scholar 

  210. 210.

    D. Schuch, contributed paper in New Frontiers in Theoretical Physics, Vol. I, T. Gill, ed. (Hadronic Press, Palm Harbor, 1996), p. 113; D. L. Schuch, Hadronic J. 19, 505 (1996).

    Google Scholar 

  211. 211.

    S. L. Adler, Phys. Rev. 17, 3212(1978).

    Google Scholar 

  212. 212.

    Cl. George, F. Henin, F. Mayene, and I. Prigogine, Hadronic J. 1, 520(1978).

    Google Scholar 

  213. 213.

    C. N. Ktorides, H. C. Myung, and R. M. Santilli, Phys. Rev. D 22, 892(1980).

    Google Scholar 

  214. 214.

    R. M. Santilli, 13, 513(1990).

  215. 215.

    R. M. Santilli, 17, 311(1994).

  216. 216.

    A. J. Kalnay, Hadronic J. 6, 1(1983).

    Google Scholar 

  217. 217.

    A. J. Kalnay and R. M. Santilli, Hadronic J. 6, 1873(1983).

    Google Scholar 

  218. 218.

    M. O. Nishioka, Nuovo Cimento A 82, 351(1984).

    Google Scholar 

  219. 219.

    G. Eder, Hadronic J. 4 (1981) and G. Eder, Hadronic J. 5, 750 (1982).

  220. 220.

    H. E. Wilhelm, contributed paper in Space, Time, and Motion: Theory and Experiments, H. E. Wilhelm and K. Liu, eds., Chinese J. Syst. Eng. Electr. 6(4) (1995).

  221. 221.

    C. A. Chatzidimitriou-Dreismann, T. Abdul-Redah, R. M. F. Streffer, and J. Mayers, Phys. Rev. Lett. 79, 2839(1997).

    Google Scholar 

  222. 222.

    C. A. Chatzidimitriou-Dreismann, T. Abdul-Redah, and B. Kolaric, J. Am. Chem. Soc. 123, 11945(2001).

    Google Scholar 

  223. 223.

    C. A. Chatzidimitriou-Dreismann, T. Abdul-Redah, R. M. F. Streffer, and J. Mayers, J. Chem. Phys. 116, 1511(2002) (see also www.ISIS.rl.ac.uk/molecularspectroscopy/EVS).

    Google Scholar 

  224. 224.

    R. M. Santilli, Hadronic J. Suppl. 1, 662(1985).

    Google Scholar 

  225. 225.

    R. M. Santilli, Journal of Dynamical Systems and Geometric Theories, in press (2003).

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Santilli, R.M. Elements of Iso-, Geno-, Hyper-Mathematics for Matter, Their Isoduals for Antimatter, and Their Applications in Physics, Chemistry, and Biology. Foundations of Physics 33, 1373–1416 (2003). https://doi.org/10.1023/A:1025601613554

Download citation

  • antimatter
  • nonlocality
  • irreversibility
  • multivaluedness