In this paper n-ary regular division associative algebras are discussed. It is shown that every operation in algebra will be endo-linearly represented over the same binary group. Schauffler like theorem proved for those algebras.

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...

This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means j-hyperideals for all positive integers 1≤j≤n and n≥3. We first introduce the notion (softly) left regularity, right intra-regularity, complete generalized regularity investigate their related properties. Several characterizations them in terms provided. Finally, relationships betwee...

Percolation theory is a subject that has been flourishing in recent decades. Because of its simple expression and rich connotation, it widely used chemistry, ecology, physics, materials science, infectious diseases, complex networks. Consider an infinite-rooted N-ary tree where each vertex assigned i.i.d. random variable. When the variable follows Bernoulli distribution, path called head run if...

Incomplete or pruned k-ary n-cube, nX3; is derived as follows. All links of dimension n 1 are left in place and links of the remaining n 1 dimensions are removed, except for one, which is chosen periodically from the remaining dimensions along the intact dimension n 1: This leads to a node degree of 4 instead of the original 2n and results in regular networks that are Cayley graphs, provided th...