This paper is written in the framework of Special Issue Mathematics entitled “Hypercompositional Algebra and Applications”, focuses on presentation essential principles hypergroup, which prominent structure hypercompositional algebra. In beginning, it reveals structural relation between two fundamental entities abstract algebra, group hypergroup. Next, presents several types hypergroups, derive...

Wildberger's construction enables us to obtain a hypergroup from random walk on special graph. We will give probability theoretic interpretation products the hypergroup. The can be identified with commutative algebra whose basis is transition matrices. estimate operator norm of such matrix and clarify relationship between their walks.

We study in this paper a generalization of the notion of a discrete hypergroup with particular emphasis on the relation with systems of orthogonal polynomials. The concept of a locally compact hypergroup was introduced by Dunkl [8], Jewett [12] and Spector [25]. It generalizes convolution algebras of measures associated to groups as well as linearization formulae of classical families of orthog...

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply the concept of fuzzy soft sets to n-ary hypergroup theory. The concepts of (∈(γ), ∈(γ) ∨ q(δ))-fuzzy soft (invertible) n-ary subhypergroups over a commutative n-ary hypergroup are intro...

Studies of musical training demonstrate functional advantages in rhythm tasks that result from enriched auditory experience. Anatomical correlates exist in brain areas involved in auditory perception, speech processing, motor control, attention, and emotion. However, these studies fail to include many classes of musicians that might undergo experience-related change. The current study examined ...