In this paper‎, ‎we first present some properties of lower and upper central series of pair of groups‎. ‎Then the notion of $n$-isoclinism for the classification of pairs of groups is introduced‎, ‎and some of the structural properties of the created classes are proved‎. ‎Moreover some interesting theorems such as Baer Theorem‎, ‎Bioch Theorem‎, ‎Hirsh Theorem for pair of groups are generalized...

The problem of placing resources in a k-ary n-cube (k > 2) is considered in this paper. For a given j 1, resources are placed such that each non-resource node is adjacent to j resource nodes. We rst prove that perfect j-adjacency placements are impossible in k-ary n-cubes if n < j < 2n. Then, we show that a perfect j-adjacency placement is possible in k-ary n-cubes when one of the following two...

Conversation is a vital tool in communication for communicating meaningful pieces of interactions. Adjacency pairs are often seen as fundamental units conversational organization. The form and purpose specific pair component, well the context beside stage conversation, all play essential roles determining meaning function an utterance. Each has special intended meaning, which cannot be fully un...

Rounded with a sleep.