Browsing by Author "Ayekple, Yao Elikem"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    On the dynamics of the Tent function-Phase diagrams
    (Modem Science Publishers, 2016-05) Kwabi P. A.; Obeng Denteh, William; Boadi, Richard Kena; Ayekple, Yao Elikem
    This paper focuses on the study of a one dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.
  • Thumbnail Image
    Item
    Representations of Finite Groups
    (2004-11-24) Ayekple, Yao Elikem
    The theory of group representation is concerned with group theory and linear algebra, with probably more of the latter than former. In Mathematics the word “representation” basically means “structure-preserving function”. Thus in group theory and ring theory at least a representation is a homomorphism. But more specifically, it should be a homomorphism from an object (group or ring) that one is trying to study to another that is in somewhat more concrete and hence, one hopes, easier to understand. The two simplest concrete kinds of groups are. firstly the group of all permutations of an arbitrary set, and secondly, the group of all invertible linear transformations on an arbitrary vector space. Groups were invented as a tool for studying symmetrical objects. These can be objects of any kind at all, if we define symmetry of an object to be a transformation of that object which preserves its essential structure then the set of all symmetries of the object forms a group. In mathematics it is always possible to regard any object as a set With Some additional structure-preserving objective function from the set to itself Composition of functions provides an operation on this set, and it is not hard to show that the group axioms must be satisfied. In order to understand groups one has to understand group actions. By considering function spaces these can be linearized, so it becomes important to understand linear actions on vector spaces, or representations of groups. Representation theory can be couched in terms of matrices or in the language of modules. We consider both approaches and then turn to the associated theory of characters.
  • Thumbnail Image
    Item
    Separating Sets for the Unitary Group U2(Fq2)
    (October,2015) Ayekple, Yao Elikem
    A separating set for a group G with respect to the group CG is a set of simultaneously diagonalisable linear operators fT 1 ; :::; Tr g of C that distinguish the invariant subspaces of CG with their eigenspaces. In this thesis, we study the character table of the irreducible representation of the unitary group G and construct the modi ed character table which consists of the eigenvalues that the class sum of each conjugacy class of G assigns to an irreducible representation of G: The separating set for G is then obtained by extracting the class sums which is associated to each irreducible character distinct pair of eigenvalues.