TY - GEN
T1 - On orthogonality preserving quadratic stochastic operators
AU - Mukhamedov, Farrukh
AU - Taha, Muhammad Hafizuddin Mohd
N1 - Publisher Copyright:
© 2015 AIP Publishing LLC.
PY - 2015/5/15
Y1 - 2015/5/15
N2 - 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.
AB - 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.
KW - Quadratic stochastic operator
KW - Volterra operator
KW - orthogonal preserving
UR - http://www.scopus.com/inward/record.url?scp=84958818848&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84958818848&partnerID=8YFLogxK
U2 - 10.1063/1.4915690
DO - 10.1063/1.4915690
M3 - Conference contribution
AN - SCOPUS:84958818848
T3 - AIP Conference Proceedings
BT - International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014
A2 - Ramli, Mohammad Fadzli
A2 - Roslan, Nurshazneem
A2 - Junoh, Ahmad Kadri
A2 - Masnan, Maz Jamilah
A2 - Kharuddin, Mohammad Huskhazrin
PB - American Institute of Physics Inc.
T2 - International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014
Y2 - 28 May 2014 through 30 May 2014
ER -