This paper develops a framework for understanding the relationships between approaches to learning adopted by students in the context of higher education and the culture of the country they were brought up in. The paper, after examining the more widely used Kolb's learning styles, opts for another categorisation, namely the so called learning approaches developed by Entwistle and others (for example,
For odd primes p and l such that the order of p modulo l is even, we determine explicitly the Jacobsthal sums φ l (v), ψ l (v), and ψ 2l (v), and the Jacobsthal-Whiteman sums φ n l (v) and φ n 2l (v), over finite fields F q such that q = p α ≡ 1 (mod 2l). These results are obtained only in terms of q and l. We apply these results pertaining to the Jacobsthal sums, to determine, for each integer n 1, the exact number of F q nrational points on the projective hyperelliptic curves aY 2 Z e−2 = bX e + cZ e (abc = 0) (for e = l, 2l), and aY 2 Z l−1 = X(bX l + cZ l ) (abc = 0), defined over such finite fields F q . As a consequence, we obtain the exact form of the ζ -functions for these three classes of curves defined over F q , as rational functions in the variable t, for all distinct cases that arise for the coefficients a, b, c. Further, we determine the exact cases for the coefficients a, b, c, for each class of curves, for which the corresponding non-singular models are maximal (or minimal) over F q .
In this paper new classes of functions namely somewhat r-continuous and somewhat r-open functions are introduced and studied by making use of regular open sets and regular closed sets. Relationship between the new classes and other classes of functions like somewhat continuous, completely continuous, almost completely continuous etc., are established besides giving examples, counter examples, properties and characterisations.
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