Today, mobile devices have become an integral part of their possessor’s life. Learning using mobile devices has the advantage of receiving educational content at the moment when it is actually needed, or when the learner feels like s/he is able to study. Moreover, mobile devices used in education can augment the learning experience by delivering further information to the learner, depending on ...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

Included among these is the sum of the squares of the characteristic numbers of P1, i.e., the sum of ihe characteristic numbers of N1 = AA*; this is the well-known unitary invariant Eapdpq of Frobenius. p,q When A is normal AA* = A*A or PU.UI*P1 = U*"P.P,U so that I= U*PU = (U*PU)2. Hence P1 = U*P,U or UP1 = POU. Conversely if UP1 = P1U we have A*A = A*A so that a matrix A is normal. when and o...