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Papers by Siti Nurlaili Karim

Research paper thumbnail of Some classes of 2-partition geometric quadratic stochastic operator on countable state space and its regularity

Kuantan, Pahang : Kulliyyah of Science, International Islamic University Malaysia, 2020, 2020

This research is designed to define and construct some classes of Geometric quadratic stochastic ... more This research is designed to define and construct some classes of Geometric quadratic stochastic operator defined on the countable state space generated by 2-partition of finite and infinite points, and to investigate their trajectory behaviour. These operators can be reinterpreted in terms of evolutionary operator of free population with arbitrary initial measure. It is shown that such operators are regular transformations through the vi

Research paper thumbnail of New Class of 2-Partition Poisson Quadratic Stochastic Operators on Countable State Space

Journal of Physics: Conference Series

The idea of quadratic stochastic operator (QSO) which was originally introduced by Bernstein in t... more The idea of quadratic stochastic operator (QSO) which was originally introduced by Bernstein in the early 20th century through his work on population genetics has been significantly developed for decades to describe dynamical systems in many areas. In this research we construct the dynamical systems generated by a new class of 2-partition of Poisson QSO defined on countable state space, X = {0,1,2,…}. Our main goal is to investigate the trajectory behavior of such operators by reducing its infinite variables into a one-dimensional setting that correspond to the number of defined partitions. We present some cases of 2-measurable partition with singleton and two points of two different parameters. Measure and probability theory alongside the functional analysis will be applied to investigate the limit behavior and characteristics of fixed points. These results suggest that the QSO generated by a 2-measurable partition defined on countable state space for both singleton and two points ...

Research paper thumbnail of On nonhomogeneous geometric quadratic stochastic operators

Turkish Journal of Mathematics

In this paper, we construct a nonhomogeneous geometric quadratic stochastic operator generated by... more In this paper, we construct a nonhomogeneous geometric quadratic stochastic operator generated by 2partition ξ on countable state space X = Z *. The limiting behavior of such operator is studied. We have proved that such operator possesses the regular property.

Research paper thumbnail of A class of geometric quadratic stochastic operator on countable state space and its regularity

Malaysian Journal of Fundamental and Applied Sciences, 2019

We have constructed a Geometric quadratic stochastic operator generated by 2-partition of single... more We have constructed a Geometric quadratic stochastic operator generated by 2-partition of singleton defined on countable state space , where . We have studied the trajectory behavior of such operator for any initial measure . It is shown that such operator converges to a fixed point which indicates the existence of the strong limit of the sequence . This follows that such operator is a regular transformation.

Research paper thumbnail of Regularity of Geometric quadratic stochastic operator generated by 2-partition of infinite points

Malaysian Journal of Fundamental and Applied Sciences, 2020

In this research, we construct a class of quadratic stochastic operator called Geometric quadrati... more In this research, we construct a class of quadratic stochastic operator called Geometric quadratic stochastic operator generated by arbitrary 2-partition of infinite points on a countable state space , where . We also study the limiting behavior of such operator by proving the existence of the limit of the sequence through the convergence of the trajectory to a unique fixed point. It is established that such operator is a regular transformation.

Research paper thumbnail of Dynamics of Nonlinear Operator Generated by Lebesgue Quadratic Stochastic Operator with Exponential Measure

Mathematics and Statistics

Quadratic stochastic operator (QSO) is a

Research paper thumbnail of New class of lebesgue quadratic stochastic operators on continual state space

Kulliyyah of Allied Health Sciences, International Islamic University Malaysia, Apr 8, 2021

The theory of quadratic stochastic operator (qso) has been developed significantly since it was i... more The theory of quadratic stochastic operator (qso) has been developed significantly since it was introduced in the early of 20th century by Bernstein through his work on population genetics. In this research, we introduce a new construction of Lebesgue qso generated by 2measurable partition on the continual state space . The main aim of this research is to investigate the trajectory behaviour of such operators by reducing its variables into one-dimensional setting which correspond to the number of its measurable partition. The limit behaviour of such operators will be investigated computationally and analytically where the computational results conform to the analytical results. Measure and probability theory alongside the functional analysis will be employed to investigate the limit behaviour and characteristics of fixed points. The results showed that for measure of Lebesgue qso less than two parameters, one can find the behaviour of such operators either have fixed point or periodic point of period 2. These results suggest that the new Lebesgue qso generated by 2measurable partition can be regular or nonregular transformation depends on the given conditions

Research paper thumbnail of Some classes of 2-partition geometric quadratic stochastic operator on countable state space and its regularity

Kuantan, Pahang : Kulliyyah of Science, International Islamic University Malaysia, 2020, 2020

This research is designed to define and construct some classes of Geometric quadratic stochastic ... more This research is designed to define and construct some classes of Geometric quadratic stochastic operator defined on the countable state space generated by 2-partition of finite and infinite points, and to investigate their trajectory behaviour. These operators can be reinterpreted in terms of evolutionary operator of free population with arbitrary initial measure. It is shown that such operators are regular transformations through the vi

Research paper thumbnail of New Class of 2-Partition Poisson Quadratic Stochastic Operators on Countable State Space

Journal of Physics: Conference Series

The idea of quadratic stochastic operator (QSO) which was originally introduced by Bernstein in t... more The idea of quadratic stochastic operator (QSO) which was originally introduced by Bernstein in the early 20th century through his work on population genetics has been significantly developed for decades to describe dynamical systems in many areas. In this research we construct the dynamical systems generated by a new class of 2-partition of Poisson QSO defined on countable state space, X = {0,1,2,…}. Our main goal is to investigate the trajectory behavior of such operators by reducing its infinite variables into a one-dimensional setting that correspond to the number of defined partitions. We present some cases of 2-measurable partition with singleton and two points of two different parameters. Measure and probability theory alongside the functional analysis will be applied to investigate the limit behavior and characteristics of fixed points. These results suggest that the QSO generated by a 2-measurable partition defined on countable state space for both singleton and two points ...

Research paper thumbnail of On nonhomogeneous geometric quadratic stochastic operators

Turkish Journal of Mathematics

In this paper, we construct a nonhomogeneous geometric quadratic stochastic operator generated by... more In this paper, we construct a nonhomogeneous geometric quadratic stochastic operator generated by 2partition ξ on countable state space X = Z *. The limiting behavior of such operator is studied. We have proved that such operator possesses the regular property.

Research paper thumbnail of A class of geometric quadratic stochastic operator on countable state space and its regularity

Malaysian Journal of Fundamental and Applied Sciences, 2019

We have constructed a Geometric quadratic stochastic operator generated by 2-partition of single... more We have constructed a Geometric quadratic stochastic operator generated by 2-partition of singleton defined on countable state space , where . We have studied the trajectory behavior of such operator for any initial measure . It is shown that such operator converges to a fixed point which indicates the existence of the strong limit of the sequence . This follows that such operator is a regular transformation.

Research paper thumbnail of Regularity of Geometric quadratic stochastic operator generated by 2-partition of infinite points

Malaysian Journal of Fundamental and Applied Sciences, 2020

In this research, we construct a class of quadratic stochastic operator called Geometric quadrati... more In this research, we construct a class of quadratic stochastic operator called Geometric quadratic stochastic operator generated by arbitrary 2-partition of infinite points on a countable state space , where . We also study the limiting behavior of such operator by proving the existence of the limit of the sequence through the convergence of the trajectory to a unique fixed point. It is established that such operator is a regular transformation.

Research paper thumbnail of Dynamics of Nonlinear Operator Generated by Lebesgue Quadratic Stochastic Operator with Exponential Measure

Mathematics and Statistics

Quadratic stochastic operator (QSO) is a

Research paper thumbnail of New class of lebesgue quadratic stochastic operators on continual state space

Kulliyyah of Allied Health Sciences, International Islamic University Malaysia, Apr 8, 2021

The theory of quadratic stochastic operator (qso) has been developed significantly since it was i... more The theory of quadratic stochastic operator (qso) has been developed significantly since it was introduced in the early of 20th century by Bernstein through his work on population genetics. In this research, we introduce a new construction of Lebesgue qso generated by 2measurable partition on the continual state space . The main aim of this research is to investigate the trajectory behaviour of such operators by reducing its variables into one-dimensional setting which correspond to the number of its measurable partition. The limit behaviour of such operators will be investigated computationally and analytically where the computational results conform to the analytical results. Measure and probability theory alongside the functional analysis will be employed to investigate the limit behaviour and characteristics of fixed points. The results showed that for measure of Lebesgue qso less than two parameters, one can find the behaviour of such operators either have fixed point or periodic point of period 2. These results suggest that the new Lebesgue qso generated by 2measurable partition can be regular or nonregular transformation depends on the given conditions