Izzat Qaralleh

On -Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior

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. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We study -QSO defined on 2D simplex. We first classify -QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.

Genetic Volterra algebras and their derivations

ABSTRACT The present paper is devoted to genetic Volterra algebras. We first study characters of such algebras. We fully describe associative genetic Volterra algebras, in this case all derivations are trivial. In general setting, i.e., when the algebra is not associative, we provide a sufficient condition to get trivial derivation on generic Volterra algebras. Furthermore, we describe all derivations of three dimensional generic Volterra algebras, which allowed us to prove that any local derivation is a derivation of the algebra.

On Derivations Of Genetic Algebras

A genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. In application of genetics this algebra often has a basis corresponding to genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. In this paper, we find the connection between the genetic algebras and evolution algebras. Moreover, we prove the existence of nontrivial derivations of genetic algebras in dimension two.

On Genetic and Evolution Algebras

The genetic and evolution algebras generally are non-associative algebra. The concept of evolution and genetic algebras were introduced to answer the question what non-Mendelian genetics offers to mathematics. This paper we review some results of evolution and genetic algebras.

Classification of ξ(s)-Quadratic Stochastic Operators on 2D simplex

In this paper we introduce a new class of quadratic stochastic operators called sξ-QSO. We classify such operators on 2D-simplex, into six non-isomorphic classes, with respect to their conjugacy and renumeration of the coordinates.