An investigation into homotopy of continuous functions

A homotopy is a continuous one-parameter family of continuous functions. This enquiry sought to find out how the various forms ranging from paths, inverses, reflexivity, symmetry and transitivity and other instances could be given in descriptive survey

Comparative analysis between homotopy group and homology group

This paper seeks to demonstrate the relation between homology group and homotopy group. The result in this paper is a construction of the homology of a complex torus

Aninvestigation Of Winding Number Of A Closed Planar Curve

This paper examines winding number of a closed planar curve through various aspects. It is related to a range on an arc in the complex plane and a point not in the range. Functions of such natures are considered to be continuous real-valued functions. Conclusion was drawn by naming a number of areas of applications

A comprehensive approach to geometric simplexes

This paper is an expository research to simplexes. The work focuses on how simplexes are created. It also looked at how complete graphs are treated as simplexes. We further present an important theorem and its proof

Periodic Point as a Recurrent Formation Using the Logistic Function: A Survey

In topological dynamical systems (TDS), recurrence (periodic–like recurrence) is one of the important concepts in its studies but one major problem is the inability to demonstrate and/or illustrate its formation in the orbit structure of system from a topological point of view. In this paper, the logistic function was applied to demonstrate the periodic point as a recurrent formation (periodic–like recurrence) in the topological dynamical system and dynamical system. The Wolfram Alpha computational knowledge engine was used in obtaining the tables and the figures for the study through various examples of the logistic function. The study shows that period – 2 recurrence is formed when the trajectory of the function is made up of two different values that keep repeating after successive iterations as a result of the period – 2 orbits when the parameter of the function is between 3 and 3.45. The study again shows that when the parameter of the function is greater than 3.83 there is a period – 3 point hence the formation of other periodic points. Convincingly, beyond this period – 3 is another subsequent period called the period-doubling cascade leading into chaos. This period-doubling asserts that other periodic–like recurrences are also present, hence period –n  recurrent exists. &nbsp

An Epidemiological Model for Sexual Activities

An epidemiological model depicting the dynamics of sexual activities among male lecturers is analysed in thisstudy. The model is a mime of the Susceptible -Infected -Recovered (SIR) model. Illegal sexual relationship bymale lectures is considered as a disease called LESEX for the purpose of this research. The model suggeststhat the recruitment of new male lecturers play a significant role in the reduction of LESEX. However, thebasic reproductive number is not enough to predict whether or not LESEX will persist among male lecturerson university campus

On the Regularization-Homotopy Analysis Method for Linear and Nonlinear Fredholm Integral Equations of the First Kind

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

Analytical Consideration of Growth in Population via Homological Invariant in Algebraic Topology

This paper presents an abstract approach of analysing population growth in the field of algebraic topology using the tools of homology theory. For a topological space X and any point vn∈X, where vn is the n-dimensional surface, the group η=X,vn is called population of the space X. The increasing sequence from vin∈X to vjn∈X for i<j provides the bases for the population growth. A growth in population η=X,vn occurs if vin<vjn for all vin∈X and vjn∈X. This is described by the homological invariant Hηk=1. The aim of this paper is to construct the homological invariant Hηk and use Hηk=1 to analyse the growth of the population. This approach is based on topological properties such as connectivity and continuity. The paper made extensive use of homological invariant in presenting important information about the population growth. The most significant feature of this method is its simplicity in analysing population growth using only algebraic category and transformations