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On new classes of chains of evolution algebras

Year 2021, Volume: 50 Issue: 1, 146 - 158, 04.02.2021
https://doi.org/10.15672/hujms.597790

Abstract

The paper is devoted to studying new classes of chains of evolution algebras and their time-depending dynamics and property transition.

Supporting Institution

Agencia Estatal de Investigación (Spain) and Xunta de Galicia (European FEDER support included, UE).

Project Number

MTM2016-79661-P and ED431C 2019/10

Thanks

We sincerely acknowledge Professor U.A. Rozikov for helpful discussions.

References

  • [1] V.M. Abraham, Linearizing quadratic transformations in genetic algebras, Proc. Lon- don Math. Soc. (3), 40 (2), 346–363, 1980.
  • [2] Y. Cabrera Casado, Evolution algebras, Ph.D. thesis, Universidad de Málaga, 2016, http://hdl.handle.net/10630/14175.
  • [3] M.I. Cardoso Gonçalves, D. Gonçalves, D. Martín Barquero, C. Martín González and M. Siles Molina, Squares and Associative Representations of two Dimen- sional Evolution Algebras, J. Algebra Appl., 2020, doi: https://doi.org/10.1142/ S0219498821500900.
  • [4] J.M. Casas, M. Ladra and U.A. Rozikov, A chain of evolution algebras, Linear Algebra Appl. 435 (4), 852–870, 2011.
  • [5] J.M. Casas, M. Ladra, B.A. Omirov and U.A. Rozikov, On evolution algebras, Algebra Colloq. 21 (2), 331–342, 2014.
  • [6] I.M.H. Etherington, Genetic algebras, Proc. Roy. Soc. Edinburgh, 59, 242–258, 1939.
  • [7] I.M.H. Etherington, Duplication of linear algebras, Proc. Edinburgh Math. Soc. (2), 6, 222–230, 1941.
  • [8] I.M.H. Etherington, Non-associative algebra and the symbolism of genetics, Proc. Roy. Soc. Edinburgh. Sect. B. 61, 24–42, 1941.
  • [9] O.J. Falcón, R.M. Falcón and J. Núñez, Classification of asexual diploid organisms by means of strongly isotopic evolution algebras defined over any field, J. Algebra, 472, 573–593, 2017.
  • [10] V. Glivenkov, Algèbre Mendelienne, C. R. (Doklady) Acad. Sci. URSS, 4, 385–386, 1936.
  • [11] H. Gonshor, Contributions to genetic algebras. II, Proc. Edinburgh Math. Soc. (2), 18, 273–279, 1973.
  • [12] I. Heuch, Sequences in genetic algebras for overlapping generations, Proc. Edinburgh Math. Soc. (2), 18, 19–29, 1972.
  • [13] P. Holgate, Sequences of powers in genetic algebras, J. London Math. Soc. 42, 489– 496, 1967.
  • [14] P. Holgate, Selfing in genetic algebras, J. Math. Biology, 6, 197–206, 1978.
  • [15] V.A. Kostitzin, Sur les coefficients mendéliens d’hérédité, C. R. Acad. Sci. Paris, 206, 883–885, 1938.
  • [16] Y.I. Lyubich, Mathematical structures in population genetics, Springer-Verlag, Berlin, 1992.
  • [17] G. Mendel, Experiments in plant-hybridization, 1865. The Electronic Scholarly Pub- lishing Project http://www.esp.org/foundations/genetics/classical/gm-65.pdf.
  • [18] Sh.N. Murodov, Classification dynamics of two-dimensional chains of evolution alge- bras, Internat. J. Math. 25 (2), 1450012, 23 pp., 2014.
  • [19] Sh.N. Murodov, Classification of two-dimensional real evolution algebras and dynamics of some two-dimensional chains of evolution algebras, Uzbek. Mat. Zh. 2014 (2), 102–111, 2014.
  • [20] M.L. Reed, Algebraic structure of genetic inheritance, Bull. Amer. Math. Soc. (N.S.), 34 (2), 107–130, 1997.
  • [21] O. Reiersöl, Genetic algebras studied recursively and by means of differential opera- tors, Math. Scand. 10, 25–44, 1962.
  • [22] U.A. Rozikov and Sh.N. Murodov, Dynamics of two-dimensional evolution algebras, Lobachevskii J. Math. 34 (4), 344–358, 2013.
  • [23] U.A. Rozikov and J.P. Tian, Evolution algebras generated by Gibbs measures, Lobachevskii J. Math. 32 (4), 270–277, 2011.
  • [24] R.D. Schafer, An introduction to nonassociative algebras, Academic Press, New York, 1966.
  • [25] A. Serebrowsky, On the properties of the Mendelian equations, C. R. (Doklady) Acad. Sci. URSS 2, 33–39, 1934 (in Russian).
  • [26] J.P. Tian, Evolution algebras and their applications, Lecture Notes in Mathematics 1921, Springer-Verlag, Berlin, 2008.
  • [27] J.P. Tian and P. Vojtechovsky, Mathematical concepts of evolution algebras in non- Mendelian genetics, Quasigroups Related Systems 14, 111–122, 2006.
  • [28] A. Wörz-Busekros, Algebras in genetics, Lecture Notes in Biomathematics 36, Springer-Verlag, Berlin-New York, 1980.
Year 2021, Volume: 50 Issue: 1, 146 - 158, 04.02.2021
https://doi.org/10.15672/hujms.597790

Abstract

Project Number

MTM2016-79661-P and ED431C 2019/10

References

  • [1] V.M. Abraham, Linearizing quadratic transformations in genetic algebras, Proc. Lon- don Math. Soc. (3), 40 (2), 346–363, 1980.
  • [2] Y. Cabrera Casado, Evolution algebras, Ph.D. thesis, Universidad de Málaga, 2016, http://hdl.handle.net/10630/14175.
  • [3] M.I. Cardoso Gonçalves, D. Gonçalves, D. Martín Barquero, C. Martín González and M. Siles Molina, Squares and Associative Representations of two Dimen- sional Evolution Algebras, J. Algebra Appl., 2020, doi: https://doi.org/10.1142/ S0219498821500900.
  • [4] J.M. Casas, M. Ladra and U.A. Rozikov, A chain of evolution algebras, Linear Algebra Appl. 435 (4), 852–870, 2011.
  • [5] J.M. Casas, M. Ladra, B.A. Omirov and U.A. Rozikov, On evolution algebras, Algebra Colloq. 21 (2), 331–342, 2014.
  • [6] I.M.H. Etherington, Genetic algebras, Proc. Roy. Soc. Edinburgh, 59, 242–258, 1939.
  • [7] I.M.H. Etherington, Duplication of linear algebras, Proc. Edinburgh Math. Soc. (2), 6, 222–230, 1941.
  • [8] I.M.H. Etherington, Non-associative algebra and the symbolism of genetics, Proc. Roy. Soc. Edinburgh. Sect. B. 61, 24–42, 1941.
  • [9] O.J. Falcón, R.M. Falcón and J. Núñez, Classification of asexual diploid organisms by means of strongly isotopic evolution algebras defined over any field, J. Algebra, 472, 573–593, 2017.
  • [10] V. Glivenkov, Algèbre Mendelienne, C. R. (Doklady) Acad. Sci. URSS, 4, 385–386, 1936.
  • [11] H. Gonshor, Contributions to genetic algebras. II, Proc. Edinburgh Math. Soc. (2), 18, 273–279, 1973.
  • [12] I. Heuch, Sequences in genetic algebras for overlapping generations, Proc. Edinburgh Math. Soc. (2), 18, 19–29, 1972.
  • [13] P. Holgate, Sequences of powers in genetic algebras, J. London Math. Soc. 42, 489– 496, 1967.
  • [14] P. Holgate, Selfing in genetic algebras, J. Math. Biology, 6, 197–206, 1978.
  • [15] V.A. Kostitzin, Sur les coefficients mendéliens d’hérédité, C. R. Acad. Sci. Paris, 206, 883–885, 1938.
  • [16] Y.I. Lyubich, Mathematical structures in population genetics, Springer-Verlag, Berlin, 1992.
  • [17] G. Mendel, Experiments in plant-hybridization, 1865. The Electronic Scholarly Pub- lishing Project http://www.esp.org/foundations/genetics/classical/gm-65.pdf.
  • [18] Sh.N. Murodov, Classification dynamics of two-dimensional chains of evolution alge- bras, Internat. J. Math. 25 (2), 1450012, 23 pp., 2014.
  • [19] Sh.N. Murodov, Classification of two-dimensional real evolution algebras and dynamics of some two-dimensional chains of evolution algebras, Uzbek. Mat. Zh. 2014 (2), 102–111, 2014.
  • [20] M.L. Reed, Algebraic structure of genetic inheritance, Bull. Amer. Math. Soc. (N.S.), 34 (2), 107–130, 1997.
  • [21] O. Reiersöl, Genetic algebras studied recursively and by means of differential opera- tors, Math. Scand. 10, 25–44, 1962.
  • [22] U.A. Rozikov and Sh.N. Murodov, Dynamics of two-dimensional evolution algebras, Lobachevskii J. Math. 34 (4), 344–358, 2013.
  • [23] U.A. Rozikov and J.P. Tian, Evolution algebras generated by Gibbs measures, Lobachevskii J. Math. 32 (4), 270–277, 2011.
  • [24] R.D. Schafer, An introduction to nonassociative algebras, Academic Press, New York, 1966.
  • [25] A. Serebrowsky, On the properties of the Mendelian equations, C. R. (Doklady) Acad. Sci. URSS 2, 33–39, 1934 (in Russian).
  • [26] J.P. Tian, Evolution algebras and their applications, Lecture Notes in Mathematics 1921, Springer-Verlag, Berlin, 2008.
  • [27] J.P. Tian and P. Vojtechovsky, Mathematical concepts of evolution algebras in non- Mendelian genetics, Quasigroups Related Systems 14, 111–122, 2006.
  • [28] A. Wörz-Busekros, Algebras in genetics, Lecture Notes in Biomathematics 36, Springer-Verlag, Berlin-New York, 1980.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Manuel Ladra 0000-0002-0543-4508

Sherzod N. Murodov This is me 0000-0002-4149-8816

Project Number MTM2016-79661-P and ED431C 2019/10
Publication Date February 4, 2021
Published in Issue Year 2021 Volume: 50 Issue: 1

Cite

APA Ladra, M., & Murodov, S. N. (2021). On new classes of chains of evolution algebras. Hacettepe Journal of Mathematics and Statistics, 50(1), 146-158. https://doi.org/10.15672/hujms.597790
AMA Ladra M, Murodov SN. On new classes of chains of evolution algebras. Hacettepe Journal of Mathematics and Statistics. February 2021;50(1):146-158. doi:10.15672/hujms.597790
Chicago Ladra, Manuel, and Sherzod N. Murodov. “On New Classes of Chains of Evolution Algebras”. Hacettepe Journal of Mathematics and Statistics 50, no. 1 (February 2021): 146-58. https://doi.org/10.15672/hujms.597790.
EndNote Ladra M, Murodov SN (February 1, 2021) On new classes of chains of evolution algebras. Hacettepe Journal of Mathematics and Statistics 50 1 146–158.
IEEE M. Ladra and S. N. Murodov, “On new classes of chains of evolution algebras”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 1, pp. 146–158, 2021, doi: 10.15672/hujms.597790.
ISNAD Ladra, Manuel - Murodov, Sherzod N. “On New Classes of Chains of Evolution Algebras”. Hacettepe Journal of Mathematics and Statistics 50/1 (February 2021), 146-158. https://doi.org/10.15672/hujms.597790.
JAMA Ladra M, Murodov SN. On new classes of chains of evolution algebras. Hacettepe Journal of Mathematics and Statistics. 2021;50:146–158.
MLA Ladra, Manuel and Sherzod N. Murodov. “On New Classes of Chains of Evolution Algebras”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 1, 2021, pp. 146-58, doi:10.15672/hujms.597790.
Vancouver Ladra M, Murodov SN. On new classes of chains of evolution algebras. Hacettepe Journal of Mathematics and Statistics. 2021;50(1):146-58.