On orthogonality preserving quadratic stochastic operators

Journal Article · Fri May 15 00:00:00 EDT 2015 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4915690· OSTI ID:22391655

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd ^[1]

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1. Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

• OSTI ID: 22391655
• Journal Information: AIP Conference Proceedings, Vol. 1660, Issue 1; Conference: ICoMEIA 2014: International Conference on Mathematics, Engineering and Industrial Applications 2014, Penang (Malaysia), 28-30 May 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BIOLOGICAL EVOLUTION
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
STOCHASTIC PROCESSES
TWO-DIMENSIONAL CALCULATIONS
VOLTERRA INTEGRAL EQUATIONS