# works

1.The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts. – http://arxiv.org/abs/1102.3596, February 17, 2011.

2.Matrix genetics and the bipolar algebra of the genetic code. – Proceedings of the 2010 International Conference on Bioinformatics and Computational Biology (Editors, Hamid Ariabnia, Quoc-Nam Tran, Associate Editors, Rui Chang, Matthew He, Andy Marsh, Ashu M. Solo, Jack Yang), 2010, CSREA Press, Vol. II, Pages 678-684 (co-author M. He).

3.The genetic code, Hadamard matrices and algebraic biology. – Journal of Biological Systems, A Special Issue on Biomedical Engineering and Applied Computing, 18, 2010, Spec01, p. 159-175, DOI: 10.1142/S0218339010003688 , http://www.worldscinet.com/jbs/18/18spec01/free-access/S0218339010003688.pdf ) (co-author M. He).

4.Matrix genetics, part 5: genetic projection operators and direct sums. – http:// arXiv:1005.5101v1 , May 18, 2010.

5.The genetic code, Hadamard matrices and inherited cycles. – International Conference on Biomedical Engineering and Computer Science (ICBECS 2010), 23-25 April 2010, Wuhan, China. Materials of the Conference, p. 7-8.

6.A Survey on Mathematical Modeling on Potential Energy Surface of Proteins. – Lecture Notes of Seminario Interdisciplinare di Matematica, Vol. IX (2010), pp. 99-110. Proceedings of the 4th International Workshop on Advanced Special Functions and Solutions of PDE’s (Edited by Alberto Cialdea, Giuseppe Dattoli, Matthew He, Hari Srivastava), (co-authors M.He, P.Ricci)

7. Articles by different authors about “Petoukhov matrices” and “Petoukhov primes” in “The On-Line Encyclopedia of Integer Sequences” http://www.research.att.com/~njas/sequences/Seis.html , A164575, A164557, A164522, A164516, A164309, A164308, A164281, A164279, A164092, A164057, A172039.

8.Symmetries in matrix genetics and Hadamard matrices of the genetic code. – Symmetry: Culture and Science, vol. 20, No. 1-4, 2009, p. 77-98 (co-author M. He).

9.Symmetries, generalized numbers and harmonic laws in matrix genetics. – Symmetry: Culture and Science, vol. 20, No. 1-4, 2009, p. 23-50 (co-author J. Kappraff)/

10. Matrix genetics, part 4: cyclic changes of the genetic 8-dimensional Yin-Yang-algebras and the algebraic models of physiological cycles. – http://arXiv:0809.2714 September 17, 2008.

11. Matrix genetics, part 3: the evolution of the genetic code from the viewpoint of the genetic octave Yin-Yang-algebra. – http://arXiv:0805.4692 , May 30, 2008.

12. Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the “Yin-Yang octave algebra”). – http://arXiv:0803.3330 , March 23, 2008.

13. Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices. – http://arXiv:0803.0888, March 6, 2008

14.The degeneracy of the genetic code and Hadamard matrices. – http://arXiv:0802.3366 , February 8, 2008.

15.Degeneracy of the genetic code and its own multi-dimensional algebra. – – XX International Congress of Genetics. Berlin, July 12-17, 2008, Abstract book, p. 209.

16.Matrix genetics, musical harmony and the genetic matrices of hydrogen bonds. – XX International Congress of Genetics. Berlin, July 12-17, 2008, Abstract book, p. 209.

17.Harmony of living nature, symmetries of genetic systems and matrix genetics. – International journal of integrative medicine, 2007, v. 1, №1, p.41-43 (co-author M. He).

18.Bioinformatics: matrix genetics, algebras of the genetic code and biоlogical harmony. – Symmetry: Culture and Science, v. 17, №1-4, 2006, р.253-291.

19.3D modeling in the field of biological prosthetics. – Symmetry: Culture and Science, v. 17, 2006, p. 239-248 (co-author V.M.Utenkov)

20.Geometric properties of genetic code and the symbolic system of the ancient Chinese “Book of changes”. Genoart. – “MADI. Art periodical” №8, 2006, с. 56-57.

21.Hadamard matrices and quint matrices in matrix presentations of molecular genetic systems. – Symmetry: Culture and Science, Vol. 16, No. 3, 2005, p. 247-266.

22.Symmetries and tensors of genetic codes. A bioinformatic approach to the geometrization of biology. – Proceedings of FIS2005, The Third Conference on the Foundations of Information Science, Paris, July 4-7, 2005. Editor: Michel Petitjean. Online Edition, ISBN 3-906980-17-0, Published in Basel, Switzerland.

23.Foreword to special issue “International Conference on Bioinformatics and its Applications – 2004”. – Journal of Biological Systems, v. 12, December 2004, p. 1-3 (co-authors D. Brutlag, M.He).

24.Foreword to «Advances in Bioinformatics and its Applications”. – «Advances in Bioinformatics and its Applications” (editors – M.He, G.Narasimhan, S.Petoukhov), ISBN 981-256-148-X, Proceedings of the International Conference (Florida, USA, 16-19 December 2004), Series in Mathematical Biology and Medicine, v.8, 2005, pp.V-VII, New Jersey–London-Singapore-Beijing, World Scientific, ISBN 981-256-148-X (co-authors M.He, G.Narasimhan).

25.The rules of degeneracy and segregations in genetic codes. The chronocyclic conception and parallels with Mendel’s laws. – “Advances in Bioinformatics and its Applications” (editors – M.He, G.Narasimhan, S.Petoukhov), Proceedings of the International Conference (Florida, USA, 16-19 December 2004), Series in Mathematical Biology and Medicine, v.8, 2005, pp.512-532, New Jersey–London-Singapore-Beijing, World Scientific, ISBN 981-256-148-X.

26.Genetic Code, Hamming Distance and Stochastic Matrices. – Bulletin of Mathematical Biology, 2004, v. 66, p. 1405-1421 (co-authors He M., Ricci P.).

27. Influence of Well-Ordered Magnetic-Domain Structures on Biomechanical Characteristics and on Symmetries of Biological Objects. – Symmetry: Culture & Science, vol. 14-15, part 1, 2003-2004, pp. 349-354 (co-authors R.Abdumalikov, E.Bragina, G.Diatchina, D.Fedorova, O. Kolomiets, O.Kuzovlev).

28. 3D modeling and symmetrological analysis of biotechnical systems. – Symmetry: Culture & Science, vol. 14-15, part 1, 2003-2004, pp. 309-310 (co-authors K.V.Frolov, V.M.Utenkov).

29. Attributive conception of genetic code, its bi-periodic tables and problem of unification bases of biological languages. – Symmetry: Culture & Science, vol. 14-15, part 1, 2003-2004, pp. 281-307.

30. Editorial. – Symmetry in Genetic Information, ed. Petoukhov S.V. (2001), special double issue of the journal “Symmetry: Culture and Science”, v.12, #3-4, 245-246 p.

31. Petoukhov S.V. Matrix Genetics and Algebraic Properties of the Multi-Level System of Genetic Alphabets. – Neuroquantology, 2011, Vol 9, No 4, p. 60-81. http://www.neuroquantology.

33. Genetic Codes 1: binary sub-alphabets, bi-symmetric matrices and golden section. – Symmetry in Genetic Information, ed. Petoukhov S.V. (2001), ISBN 963216 242 0, special double issue of the journal “Symmetry: Culture and Science”, Budapest: International Symmetry Foundation, v. 12, #3-4, pp. 255-274

34. Genetic code and the Ancient Chinese “Book of Changes”. – Symmetry: Culture & Science, vol. 10, №3-4, 1999, р. 211-226.

35. Highest symmetries and biological algorithms. – Symmetry: Culture & Science, vol. 6, ¹ 3, 1995, p. 426-427.

36. Highest biosymmetries and the concept of replicational morphogenesis. – Symmetry: Culture & Science, vol. 3, ¹ 1, 1992, р. 60-61.

37.Symmetric-algorithmic properties of regular biostructures. – Symmetry: Culture & Science, vol. 1, ¹ 3, 1990, р.295-312.

38. Highest symmetries and iterative algorithms in self-organization of living matter. – Abstracts of International symposium “Symmetry of Structure”, 15-19.08.1989, Budapest, vol. 2, p. 423-426.

39. Non-Euclidean geometries and algorithms of living bodies. – Computers & Mathematics with Applications, v. 17, № 4-6, 1989, p. 505-534.

40. On the application of computerized tomography to biodynamics. – Man under vibration/ Proceeding of the second International CISM-IFTOMM Symposium, Moscow, USSR, April 8-12, 1985, p. 275-279.

41. Investigations on Non-Euclidean biomechanics. Projective geometry, Fibonacci numbers and the kinematic scheme of human body. – Biomechanics-7, VII, Warszawa, 1981, p. 603-607.1.The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts. – http://arxiv.org/abs/1102.3596, February 17, 2011.

42.Matrix genetics and the bipolar algebra of the genetic code. – Proceedings of the 2010 International Conference on Bioinformatics and Computational Biology (Editors, Hamid Ariabnia, Quoc-Nam Tran, Associate Editors, Rui Chang, Matthew He, Andy Marsh, Ashu M. Solo, Jack Yang), 2010, CSREA Press, Vol. II, Pages 678-684 (co-author M. He).

43.The genetic code, Hadamard matrices and algebraic biology. – Journal of Biological Systems, A Special Issue on Biomedical Engineering and Applied Computing, 18, 2010, Spec01, p. 159-175, DOI: 10.1142/S0218339010003688 , http://www.worldscinet.com/jbs/18/18spec01/free-access/S0218339010003688.pdf ) (co-author M. He).

44.Matrix genetics, part 5: genetic projection operators and direct sums. – http:// arXiv:1005.5101v1 , May 18, 2010.

55.The genetic code, Hadamard matrices and inherited cycles. – International Conference on Biomedical Engineering and Computer Science (ICBECS 2010), 23-25 April 2010, Wuhan, China. Materials of the Conference, p. 7-8.

46.A Survey on Mathematical Modeling on Potential Energy Surface of Proteins. – Lecture Notes of Seminario Interdisciplinare di Matematica, Vol. IX (2010), pp. 99-110. Proceedings of the 4th International Workshop on Advanced Special Functions and Solutions of PDE’s (Edited by Alberto Cialdea, Giuseppe Dattoli, Matthew He, Hari Srivastava), (co-authors M.He, P.Ricci)

47. Articles by different authors about “Petoukhov matrices” and “Petoukhov primes” in “The On-Line Encyclopedia of Integer Sequences” http://www.research.att.com/~njas/sequences/Seis.html , A164575, A164557, A164522, A164516, A164309, A164308, A164281, A164279, A164092, A164057, A172039.

48.Symmetries in matrix genetics and Hadamard matrices of the genetic code. – Symmetry: Culture and Science, vol. 20, No. 1-4, 2009, p. 77-98 (co-author M. He).

49.Symmetries, generalized numbers and harmonic laws in matrix genetics. – Symmetry: Culture and Science, vol. 20, No. 1-4, 2009, p. 23-50 (co-author J. Kappraff)/

50. Matrix genetics, part 4: cyclic changes of the genetic 8-dimensional Yin-Yang-algebras and the algebraic models of physiological cycles. – http://arXiv:0809.2714 September 17, 2008.

51. Matrix genetics, part 3: the evolution of the genetic code from the viewpoint of the genetic octave Yin-Yang-algebra. – http://arXiv:0805.4692 , May 30, 2008.

52. Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the “Yin-Yang octave algebra”). – http://arXiv:0803.3330 , March 23, 2008.

53. Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices. – http://arXiv:0803.0888, March 6, 2008

54.The degeneracy of the genetic code and Hadamard matrices. – http://arXiv:0802.3366 , February 8, 2008.

55.Degeneracy of the genetic code and its own multi-dimensional algebra. – – XX International Congress of Genetics. Berlin, July 12-17, 2008, Abstract book, p. 209.

56.Matrix genetics, musical harmony and the genetic matrices of hydrogen bonds. – XX International Congress of Genetics. Berlin, July 12-17, 2008, Abstract book, p. 209.

57.Harmony of living nature, symmetries of genetic systems and matrix genetics. – International journal of integrative medicine, 2007, v. 1, №1, p.41-43 (co-author M. He).

58.Bioinformatics: matrix genetics, algebras of the genetic code and biоlogical harmony. – Symmetry: Culture and Science, v. 17, №1-4, 2006, р.253-291.

59.3D modeling in the field of biological prosthetics. – Symmetry: Culture and Science, v. 17, 2006, p. 239-248 (co-author V.M.Utenkov)

60.Geometric properties of genetic code and the symbolic system of the ancient Chinese “Book of changes”. Genoart. – “MADI. Art periodical” №8, 2006, с. 56-57.

61.Hadamard matrices and quint matrices in matrix presentations of molecular genetic systems. – Symmetry: Culture and Science, Vol. 16, No. 3, 2005, p. 247-266.

62.Symmetries and tensors of genetic codes. A bioinformatic approach to the geometrization of biology. – Proceedings of FIS2005, The Third Conference on the Foundations of Information Science, Paris, July 4-7, 2005. Editor: Michel Petitjean. Online Edition, ISBN 3-906980-17-0, Published in Basel, Switzerland.

63.Foreword to special issue “International Conference on Bioinformatics and its Applications – 2004”. – Journal of Biological Systems, v. 12, December 2004, p. 1-3 (co-authors D. Brutlag, M.He).

64.Foreword to «Advances in Bioinformatics and its Applications”. – «Advances in Bioinformatics and its Applications” (editors – M.He, G.Narasimhan, S.Petoukhov), ISBN 981-256-148-X, Proceedings of the International Conference (Florida, USA, 16-19 December 2004), Series in Mathematical Biology and Medicine, v.8, 2005, pp.V-VII, New Jersey–London-Singapore-Beijing, World Scientific, ISBN 981-256-148-X (co-authors M.He, G.Narasimhan).

65.The rules of degeneracy and segregations in genetic codes. The chronocyclic conception and parallels with Mendel’s laws. – “Advances in Bioinformatics and its Applications” (editors – M.He, G.Narasimhan, S.Petoukhov), Proceedings of the International Conference (Florida, USA, 16-19 December 2004), Series in Mathematical Biology and Medicine, v.8, 2005, pp.512-532, New Jersey–London-Singapore-Beijing, World Scientific, ISBN 981-256-148-X.

66.Genetic Code, Hamming Distance and Stochastic Matrices. – Bulletin of Mathematical Biology, 2004, v. 66, p. 1405-1421 (co-authors He M., Ricci P.).

67. Influence of Well-Ordered Magnetic-Domain Structures on Biomechanical Characteristics and on Symmetries of Biological Objects. – Symmetry: Culture & Science, vol. 14-15, part 1, 2003-2004, pp. 349-354 (co-authors R.Abdumalikov, E.Bragina, G.Diatchina, D.Fedorova, O. Kolomiets, O.Kuzovlev).

68. 3D modeling and symmetrological analysis of biotechnical systems. – Symmetry: Culture & Science, vol. 14-15, part 1, 2003-2004, pp. 309-310 (co-authors K.V.Frolov, V.M.Utenkov).

69. Attributive conception of genetic code, its bi-periodic tables and problem of unification bases of biological languages. – Symmetry: Culture & Science, vol. 14-15, part 1, 2003-2004, pp. 281-307.

70. Editorial. – Symmetry in Genetic Information, ed. Petoukhov S.V. (2001), special double issue of the journal “Symmetry: Culture and Science”, v.12, #3-4, 245-246 p.

71. Genetic Codes II: Numeric rules of degeneracy and a chronocyclic theory. – Symmetry in Genetic Information, ed. Petoukhov S.V. (2001), ISBN 963216 242 0, special double issue of the journal “Symmetry: Culture and Science”, Budapest: International Symmetry Foundation, v.12, #3-4, pp. 275-306.

72. Genetic Codes 1: binary sub-alphabets, bi-symmetric matrices and golden section. – Symmetry in Genetic Information, ed. Petoukhov S.V. (2001), ISBN 963216 242 0, special double issue of the journal “Symmetry: Culture and Science”, Budapest: International Symmetry Foundation, v. 12, #3-4, pp. 255-274

73. Genetic code and the Ancient Chinese “Book of Changes”. – Symmetry: Culture & Science, vol. 10, №3-4, 1999, р. 211-226.

74. Highest symmetries and biological algorithms. – Symmetry: Culture & Science, vol. 6, ¹ 3, 1995, p. 426-427.

75. Highest biosymmetries and the concept of replicational morphogenesis. – Symmetry: Culture & Science, vol. 3, ¹ 1, 1992, р. 60-61.

76.Symmetric-algorithmic properties of regular biostructures. – Symmetry: Culture & Science, vol. 1, ¹ 3, 1990, р.295-312.

77. Highest symmetries and iterative algorithms in self-organization of living matter. – Abstracts of International symposium “Symmetry of Structure”, 15-19.08.1989, Budapest, vol. 2, p. 423-426.

78. Non-Euclidean geometries and algorithms of living bodies. – Computers & Mathematics with Applications, v. 17, № 4-6, 1989, p. 505-534.

79. On the application of computerized tomography to biodynamics. – Man under vibration/ Proceeding of the second International CISM-IFTOMM Symposium, Moscow, USSR, April 8-12, 1985, p. 275-279.

80. Investigations on Non-Euclidean biomechanics. Projective geometry, Fibonacci numbers and the kinematic scheme of human body. – Biomechanics-7, VII, Warszawa, 1981, p. 603-607.