On new classes of chains of evolution algebras
Year 2021,
Volume: 50 Issue: 1, 146 - 158, 04.02.2021
Manuel Ladra
,
Sherzod N. Murodov
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
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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.
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1936.
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Math. Soc. (2), 18, 19–29, 1972.
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496, 1967.
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883–885, 1938.
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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
Manuel Ladra
,
Sherzod N. Murodov
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.