in this paper, two new hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. it is shown that finite screw motions in minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual lorentzian space. moreover, by means of hamilton operators, screwmotion is obtained in 3-dimensional minkowski space 3r1

in this paper, we de ne the concepts of general fuzzy recognizer, language recognized by a general fuzzy recognizer, the accessible and the coac- cessible parts of a general fuzzy recognizer and the reversal of a general fuzzy recognizer. then we obtain the relationships between them and construct a topology and some hypergroups on a general fuzzy recognizer.

In this paper, we present some connections between tree automaton theory and hyperstructure theory. In this regard, at first we construct some hyperoperations on the set of trees and, specially, prove that one of them creates a join space. Also, we define a hyperoperation on the states of a tree automaton and, based on the properties of the tree automaton, we show that the proposed hyperoperati...

We present an explicit product formula for the spherical functions of the compact Gelfand pairs (G,K1) = (SU(p+ q), SU(p)× SU(q)) with p ≥ 2q, which can be considered as the elementary spherical functions of one-dimensional K-type for the Hermitian symmetric spaces G/K with K = S(U(p)× U(q)). Due to results of Heckman, they can be expressed in terms of Heckman-Opdam Jacobi polynomials of type B...

Sunder and Wildberger (J. Algebr. Comb. 18, 135–151, 2003) introduced the notion of actions of finite hypergroups, and studied maximal irreducible actions and *-actions. One of the main results of Sunder and Wildberger states that if a finite hypergroup K admits an irreducible action which is both a maximal action and a *action, then K arises from an association scheme. In this paper we will fi...

in this paper we study two important concepts, i.e. the direct andthe inverse limit of hyperstructures associated with fuzzy sets of type 2, andshow that the direct and the inverse limit of hyperstructures associated withfuzzy sets of type 2 are also hyperstructures associated with fuzzy sets of type 2.

In this paper, we have generalized the definition of vector space by considering the group as a canonical $m$-ary hypergroup, the field as a krasner $(m,n)$-hyperfield and considering the multiplication structure of a vector by a scalar as hyperstructure. Also we will be consider a normed $m$-ary hypervector space and introduce the concept of convergence of sequence on $m$-ary hypernormed space...

In this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (K, ?) are equivalent. For a normal subgroup H of K, we define a weight function ?? on KIH and obtain connection between left amenability of (K, ?) and (K|H, ??). Let H be a compact subhypergroup of K. We define the weight function on K||H and obtain connection...

in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...