This paper investigates the question of when a finite hypergroup with three elements is strong, that is satisfies the condition that its dual signed hypergroup is actually a hypergroup. We classify hermitian hypergroups of order three by weight into two dimensional families and show that the algebraic conditions arising from duality yield four interesting curves in the plane which bound the cha...

layer The Information Models in the abstract layer hold the fundamental modeling concepts, which are independent of a particular problem or domain and can therefore be universally applied. They describe the design guidelines (design pattern) for the construction of the other sub models in the DIM. Models like n-ary relationship, part-whole relationship, graph model and system model belong to th...

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...

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and in which is a proper sub-hypergroup. The latter class includes family of 1-hypergroups, reduces to singleton, therefore trivial group. However, very little known about hypergroups that are neither 1-hypergroups nor belong first class. goal this work take step classifying G-hypergroups...

A homomorphism of a hypergroup (H, ◦) is a function f : H → H satisfying f(x ◦ y) ⊆ f(x) ◦ f(y) for all x, y ∈ H. A homomorphism of a hypergroup (H, ◦) is called an epimorphism if f(H) = H. Denote by Hom(H, ◦) and Epi(H, ◦) the set of all homomorphisms and the set of all epimorphisms of a hypergroup (H, ◦), respectively. In this paper, the elements of Hom(Zn, ◦m) and Epi(Zn, ◦m) are characteriz...

Conformal inclusions of chiral conformal field theories, or more generally quantum are described in the von Neumann algebraic setting by nets subfactors, possibly with infinite Jones index if one takes non-rational theories into account. With this situation mind, we study a purely subfactor theoretical context certain class braided discrete subfactors an additional commutativity constraint, tha...

An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. An n-ary quasigroup Q is (permutably) reducible if Q(x1, . . . , xn) = P ( R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n) ) where P and R are (n−k+1)-ary and k-ary quasigroups, σ is a permutation, a...

In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. We show that the splicing algebras are an n-ary envelope for algebras of DNA recombinati...