This paper identified a new and more generalised generating function for the Aunu Patterns which is based on the methods employed earlier by Garba. It also identified and discussed some other theoretic properties of the Aunu Patterns and Aunu Groups especially in relation to integer modulo groups.

The derivation of Block Nyström type Method (BNTM) which is not normally used as numerical integrator of boundary value problems 184 E.O. Adeyefa et al. (BVPs) is considered and directly applied to solve both initial value problems (IVPs) and BVPs in ordinary differential equations (ODEs). Collocation technique is adopted in the derivation of the BNTM which is applied as simultaneous integrator to fourth order ODEs. The BNTM possesses the desirable feature of being self-starting as the implementation is in block form. The paper concludes by solving Numerical examples which establish the effectiveness and accuracy of the method. The superiority of BNTM is established by the numerical values presented.

5ABSTRACT: This paper presents some backgrounds research on association scheme using a class of (123)-avoiding pattern of Aunu numbers as an application area. It also attempts to highlight some further applications in other set structures. The finding in this research has shown that there is some interrelationship between the succession scheme used in generating Aunu numbers and the concept of association scheme. This research also shows us that the Aunu patterns can be used in design theory.

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Finite fields is considered to be the most widely used algebraic structures today due to its applications in cryptography, coding theory, error correcting codes among others. This paper reports the use of extended Euclidean algorithm in computing the greatest common divisor (gcd) of Aunu binary polynomials of cardinality seven. Each class of the polynomial is permuted into pairs until all the succeeding classes are exhausted. The findings of this research reveals that the gcd of most of the pairs of the permuted classes are relatively prime. This results can be used further in constructing some cryptographic architectures that could be used in design of strong encryption schemes.