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Papers by Patrick Akwasi anamuah Mensah

Elixir International Journal), 2018

In this research we use the logistic function to demonstrate the existence of a stationary point... more In this research we use the logistic function to demonstrate the existence of a stationary
point as a type of a non-wandering set in topological dynamical systems or dynamical
systems without any loss of generality.

The purpose of the study was to find out the effect of leadership styles of Headteachers on the a... more The purpose of the study was to find out the effect of leadership styles of Headteachers on the academic performance of students. The study was a multi-pronged approach, commonly referred to as triangulation combining both qualitative and quantitative research methods. The samples that provided data were from Headteachers, Teachers, Parents, Students and Educational authorities at the district. Data were collected through questionnaire and the analysis of the questions was done using Statistical Package for Social Sciences (SPSS); and in order eliminate errors in the data entry, all data were re-entered through the Epi-Info software interface. The results were also subjected to cross tabulations to bring out details of the results in relation to the independent variables (leadership styles). Over 60% of respondents (271) maintained that the leadership styles of Headteachers have some influence on academic performance of students. The conclusion and Original Research Article

This research aimed at finding out students and teachers perception about factors contributing to... more This research aimed at finding out students and teachers perception about factors contributing to the decline in students' performance in mathematics in Asesewa Senior Secondary School in Manyakrobo District (Upper). The researchers narrowed their attention on how do students and teachers perceive resources motivation to learning as a factor inhibiting students' performance in mathematics. Descriptive survey design was used because the study objective was to collect information from respondents on the bases of what contributes to the poor performance of students in mathematics in the District. A total sample size of 150 mathematics teachers and students were used for study. Data collection was done through distribution of questionnaire and were analyzed using SPSS. The major findings of the study were: male performance been better than female performance but in cases where motivations were made in any form, the female performance overtook or came to level equal to the male performance. Also mathematics teachers and students showed a very strong positive response that student's motivation to learn mathematics will be one of the better factors towards the improvement of student's performance in mathematics. Finally the study reveals that, with respect to gender on the part of teachers and students there were no significant difference in the perception of males and females on the motivation to learn.

In an attempt to discover the effect of recurrence on the topological dynamics, a nonlinear funct... more In an attempt to discover the effect of recurrence on the topological dynamics, a nonlinear function whose regime of periodicity amounts to recurrence was considered, thus the logistic function. This research seeks to study the logistic function as to how it really behaves. In the field of dynamics most especially this function in terms of discrete form has been studied. Logistic equation as a model based on population growth was initially originated by the famous Pierre-Francios Verhulst. It is a continuous form written as í µí±‘í µí±¥ í µí±‘í µí±¡ = í µí±Ÿ(í µí±¥ − í µí±¥ 2), which depend on time. It can be restructured from the continuous form into a discrete form known as logistic function, written as; í µí±¥ í µí±›+1 = í µí±Ÿí µí±¥ í µí±› (1 − í µí±¥ í µí±›), with í µí±› = 0,1,2,3 … … ,í µí±¥ í µí±› is

Fredholm integral equations of the first kind are considered by applying regularization method an... more Fredholm integral equations of the first kind are considered by applying regularization method and the homotopy analysis method. This kind of integral equations are considered as an ill-posed problem and for this reason needs an effective method in solving them. This method first transforms a given Fredholm integral equation of the first kind to the second kind by the regularization method and then solves the transformed equation using homotopy analysis method. Approximation of the solution will be of much concern since it is not always the case to get the solution to converge and the existence of the solution is not always guaranteed as this kind of Fredholm integral equation is not well-posed.

The logistic function as nonlinear function/equation has behaviors that translate from one regime... more The logistic function as nonlinear function/equation has behaviors that translate from one regime to another regime. The behaviors move from periodic to chaotic depending on the parameter in the function. The purpose of this research is to use graphs to show the behavior of the function and the route it takes to chaos.

Recurrence as behaviour in the dynamical system is also a state which happens as a result of an o... more Recurrence as behaviour in the dynamical system is also a state which happens as a result of an outcome of a point which does return to its initial state. But in dynamical system the most simple and easy way to study regime in one dimension is the logistic function. In this study we seek to understudy the recurrence as a full strong state from the nature or behaviour of the logistic function, where the periodic orbits as behaviour the logistic function is considered. A point can only be termed as recurrent if it is in its own future state. A periodic orbit returns infinitely often to each point on the orbit. And so it is clear that an orbit is recurrent when it returns repeatedly to each neighbourhood of its initial position. Recurrence as in dynamical system is a result of periodic formation which is a movement that returns back to the original state or position at a constant rate. A systematic example for each periodic point from the logistic function relative to a control parameter is discussed. Different iterations tables, diagrams (graphs) for against , tables of stability of periodic nature which shows relative range of the control parameter and are discussed. Through graphical illustrations and algebraic approach, the study showed that in the formation of recurrence through logistic function, the parameter played a major role and not all the periodic points Review Article Mensah et al.; ARJOM, 4(3): 1-13, 2017; Article no.ARJOM.32588 2 (orbits) lead to recurrent formation. The study also showed that unstable behaviour of the logistic function when = 4, ends the periodic behaviour, hence the absence of recurrence. And the absence of recurrent and the unstable nature of system bring about chaos.

Thesis Chapters by Patrick Akwasi anamuah Mensah

Elixir International Journal), 2018

In this research we use the logistic function to demonstrate the existence of a stationary point... more In this research we use the logistic function to demonstrate the existence of a stationary
point as a type of a non-wandering set in topological dynamical systems or dynamical
systems without any loss of generality.

The purpose of the study was to find out the effect of leadership styles of Headteachers on the a... more The purpose of the study was to find out the effect of leadership styles of Headteachers on the academic performance of students. The study was a multi-pronged approach, commonly referred to as triangulation combining both qualitative and quantitative research methods. The samples that provided data were from Headteachers, Teachers, Parents, Students and Educational authorities at the district. Data were collected through questionnaire and the analysis of the questions was done using Statistical Package for Social Sciences (SPSS); and in order eliminate errors in the data entry, all data were re-entered through the Epi-Info software interface. The results were also subjected to cross tabulations to bring out details of the results in relation to the independent variables (leadership styles). Over 60% of respondents (271) maintained that the leadership styles of Headteachers have some influence on academic performance of students. The conclusion and Original Research Article

This research aimed at finding out students and teachers perception about factors contributing to... more This research aimed at finding out students and teachers perception about factors contributing to the decline in students' performance in mathematics in Asesewa Senior Secondary School in Manyakrobo District (Upper). The researchers narrowed their attention on how do students and teachers perceive resources motivation to learning as a factor inhibiting students' performance in mathematics. Descriptive survey design was used because the study objective was to collect information from respondents on the bases of what contributes to the poor performance of students in mathematics in the District. A total sample size of 150 mathematics teachers and students were used for study. Data collection was done through distribution of questionnaire and were analyzed using SPSS. The major findings of the study were: male performance been better than female performance but in cases where motivations were made in any form, the female performance overtook or came to level equal to the male performance. Also mathematics teachers and students showed a very strong positive response that student's motivation to learn mathematics will be one of the better factors towards the improvement of student's performance in mathematics. Finally the study reveals that, with respect to gender on the part of teachers and students there were no significant difference in the perception of males and females on the motivation to learn.

In an attempt to discover the effect of recurrence on the topological dynamics, a nonlinear funct... more In an attempt to discover the effect of recurrence on the topological dynamics, a nonlinear function whose regime of periodicity amounts to recurrence was considered, thus the logistic function. This research seeks to study the logistic function as to how it really behaves. In the field of dynamics most especially this function in terms of discrete form has been studied. Logistic equation as a model based on population growth was initially originated by the famous Pierre-Francios Verhulst. It is a continuous form written as í µí±‘í µí±¥ í µí±‘í µí±¡ = í µí±Ÿ(í µí±¥ − í µí±¥ 2), which depend on time. It can be restructured from the continuous form into a discrete form known as logistic function, written as; í µí±¥ í µí±›+1 = í µí±Ÿí µí±¥ í µí±› (1 − í µí±¥ í µí±›), with í µí±› = 0,1,2,3 … … ,í µí±¥ í µí±› is

Fredholm integral equations of the first kind are considered by applying regularization method an... more Fredholm integral equations of the first kind are considered by applying regularization method and the homotopy analysis method. This kind of integral equations are considered as an ill-posed problem and for this reason needs an effective method in solving them. This method first transforms a given Fredholm integral equation of the first kind to the second kind by the regularization method and then solves the transformed equation using homotopy analysis method. Approximation of the solution will be of much concern since it is not always the case to get the solution to converge and the existence of the solution is not always guaranteed as this kind of Fredholm integral equation is not well-posed.

The logistic function as nonlinear function/equation has behaviors that translate from one regime... more The logistic function as nonlinear function/equation has behaviors that translate from one regime to another regime. The behaviors move from periodic to chaotic depending on the parameter in the function. The purpose of this research is to use graphs to show the behavior of the function and the route it takes to chaos.

Recurrence as behaviour in the dynamical system is also a state which happens as a result of an o... more Recurrence as behaviour in the dynamical system is also a state which happens as a result of an outcome of a point which does return to its initial state. But in dynamical system the most simple and easy way to study regime in one dimension is the logistic function. In this study we seek to understudy the recurrence as a full strong state from the nature or behaviour of the logistic function, where the periodic orbits as behaviour the logistic function is considered. A point can only be termed as recurrent if it is in its own future state. A periodic orbit returns infinitely often to each point on the orbit. And so it is clear that an orbit is recurrent when it returns repeatedly to each neighbourhood of its initial position. Recurrence as in dynamical system is a result of periodic formation which is a movement that returns back to the original state or position at a constant rate. A systematic example for each periodic point from the logistic function relative to a control parameter is discussed. Different iterations tables, diagrams (graphs) for against , tables of stability of periodic nature which shows relative range of the control parameter and are discussed. Through graphical illustrations and algebraic approach, the study showed that in the formation of recurrence through logistic function, the parameter played a major role and not all the periodic points Review Article Mensah et al.; ARJOM, 4(3): 1-13, 2017; Article no.ARJOM.32588 2 (orbits) lead to recurrent formation. The study also showed that unstable behaviour of the logistic function when = 4, ends the periodic behaviour, hence the absence of recurrence. And the absence of recurrent and the unstable nature of system bring about chaos.