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On Bernstein algebras which are train algebras

Published online by Cambridge University Press:  20 January 2009

Sebastian Walcher
Affiliation:
Mathematisches Insttitut der TU MünchenPostfach 202420D-8000 München 2, Germany
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The class of non-associative algebras over a field of characteristic zero named in the title is studied using a result of Ouattara [9]. As an application, the differential equation for overlapping generations in the time-continuous model is solved.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Andreoli, G., Algebre non associative e sistemi differenziati di Riccati in un problema di Genetica, Ann. Mat. Pura Appl. 49 (1960), 97116.CrossRefGoogle Scholar
2.Bernstein, S., Solution of a mathematical problem connected with the theory of heredity, Ann. Math. Statist. 13 (1942), 5361.CrossRefGoogle Scholar
3.Heuch, I., Genetic algebras and time continuous models. Theor. Pop. Bio. 4 (1973), 133144.Google Scholar
4.Holgate, P., Genetic algebras satisfying Bernstein's stationarity principle, J. London Math. Soc. (2) 9 (1975), 613623.Google Scholar
5.Lyubich, Yu. I., Basic concepts and theorems of evolution genetics of free populations, Russian Math. Surveys 26 (1971), 51123.CrossRefGoogle Scholar
6.Schafer, R. D., Structure of genetic algebras, Amer. J. Math. 71 (1949), 121135.CrossRefGoogle Scholar
7.Walcher, S., Algebras and differential equations (Hadronic Press, to appear).Google Scholar
8.Wörz-Busekros, A., Algebras in genetics (Springer Lecture Notes in Biomathematics 36, (1980)).CrossRefGoogle Scholar
9.Ouattara, M., Sur les algèbres de Bernstein qui sont des T – algèbras, Lin. Alg. Appl. 148 (1991), 171178.CrossRefGoogle Scholar