Previous |  Up |  Next

Article

Keywords:
genetic algebra; population genetics; Jordan algebra
References:
[1] Beier, W.: Biophysik. VEB Georg Thieme, Leipzig 1960.
[2] Bernstein, S.: Demonstration mathematique de la loi d’heredité de Mendel. C. R. Acad. Sci. Paris 177 (1923), 528–531.
[3] Drozd Kiričenko, Ju.: Koněčnomernyje algebry. Kiev 1980.
[4] Etherington, I. M. H.: Genetic algebras. Proc. Roy. Soc. Edinburgh 59 (1939), 242–258. MR 0000597 | Zbl 0027.29402
[5] Etherington, I. M. H.: Special train algebras. Quart. J. Math. 12 (1941), 1–8. MR 0005111 | Zbl 0027.29401
[6] Etherington, I. M. H.: Nonassociative algebra and the symbolism of genetics. Proc. Roy Soc. Edinburgh 61 (1941), 24–42. MR 0003557
[7] Etherington, I. M. H.: Duplication of linear algebras. Proc. Edinburgh Math. Soc. Ser. 2 6 (1941), 222–230. MR 0005113
[8] Glivenko, V. I.: Mendělevskaja algebra. Dokl. Akad. Nauk 13 (1936), 371–372.
[9] Gonshor, H.: Special train algebras arising in genetics. Proc. Edinburgh Math. Soc. Ser. 2 12 (1960), 41–63. MR 0124367 | Zbl 0249.17003
[10] Heuch, I.: Genetic algebras considered as elements in a vector space. Siam J. Appl. 35 (1978), 695–703. DOI 10.1137/0135058 | MR 0512179 | Zbl 0392.17013
[11] Hogben, L.: An introduction to mathematical genetics. Norton, New York 1946. MR 0019906
[12] Holgate, P.: Jordan algebras arising in population genetics. Proc. Edinburgh Math. Soc. 15 (1967), 291–294. MR 0223420 | Zbl 0153.36304
[13] Holgate, P.: Characterization of genetic algebras. J. London Math. Soc. 6 (1972), 169–174. MR 0314930
[14] Hungerford, T. V.: Algebra. Springer-Verlag, New York-Heidelberg-Berlin 1980. MR 0600654 | Zbl 0442.00002
[15] Jordan, P.: Über Verallgeneinerungsmöglichkeiten des Formalismus der Quantenmechanik. Nachr. Ges. Wiss. Göttingen (1933), 209–214.
[16] Jordan, P., Neumann, J., Wigner, E.: On an algebraic generalization of the quantum mechanical formalism. Ann. Math. 35 (1934), 29–64. DOI 10.2307/1968117 | MR 1503141 | Zbl 0061.05302
[17] Katrnoška, F: Logics that are generated by idempotents. Lobachevskii J. Math. 15 (2004), 11–19. MR 2120697 | Zbl 1060.15018
[18] Katrnoška, F., Křížek, M.: Genetický kód a teorie monoidů aneb 50 let od objevu struktury DNA. PMFA 48 (2003), 207–222.
[19] Katrnoška, F., Křížek, M.: Významné milníky matematické genetiky. Matematika–fyzika–informatika 14 (2004/05), 1–12.
[20] Ljubič, Ju. I.: Osnovnyje poňatia i teoremy evoljucionnoj genetiki svobodnych populacii. Uspekhi Mat. Nauk 161 (1971), 51–116.
[21] Ljubič, Ju. I.: Bernštejnovskije algebry. Uspekhi Mat. Nauk 32 (1977), 261–262.
[22] Ljubič, Ju. I.: Stochastičeskije algebry i někotoryje primeněnija v matematičeskoj genetike. In: Matematičeskije Metody v Biologii, Naukova dumka, Kiev 1977, 119–131.
[23] Ljubič, Ju. I.: Algebraic methods in evolutionary genetics. Biomath. J. 20 (1978), 511–529. MR 0529790
[24] Ljubič, Ju. I.: Matematičeskije struktury v populacionnoj genetike. Naukova dumka, Kiev 1983.
[25] Raffin, R.: Axiomatization des algebres genetiques. Bull. V. Sci., Acad. Roy. Belg. 17 (1951), 359–366. MR 0042400
[26] Reiersöl, O.: Genetic algebras studied recursively and by means of differential operators. Math. Scand. (1962), 25–44. MR 0137740
[27] Revoy, N.: Cube magique, La perfection a été atteinte. Science et Vie, Mars (2004), 66–68.
[28] Rybnikov, K. A.: Vvěděnije v kombinatornyj analiz. Izd. Moskovskogo Universiteta, Moskva 1985. MR 0812275
[29] Schafer, R. D.: Structure of genetic algebras. Amer. J. Math. 71 (1949), 121–135. MR 0027751 | Zbl 0034.02004
[30] Schafer, R. D.: An introduction to nonassociative algebras. Academic Press, New York-London 1966. MR 0210757 | Zbl 0145.25601
[31] Thompson, J. S., Thompson, M. W.: Genetics in medicine. W. B. Saunders Company, Philadelphia 1986, 2001.
[32] Wörz-Busekros, A.: Algebras in genetics. Springer-Verlag, Berlin 1980. MR 0599179
[33] Želazko, W.: Banach algebras. Elsevier, Amsterdam 1973. MR 0448079
[34] Želazko, W.: A characterization of multiplicative linear functionals in complex Banach algebras. Studia Math. 30 (1968), 83–85. MR 0229042
Partner of
EuDML logo