Stating a two-parameter class of examples, a — positive — answer is given to the question “Are there any nontrivial hypergroups on Z?” . 1. Background and Introduction In 1989 Zeuner [14] proved that no nontrivial hypergroups (i. e. not the group) exist on the set of real numbers R. Five years later Rösler [5] showed that by weakening the axioms by considering signed hypergroups some of these s...

Defensive JavaScript (DJS) is a typed subset of JavaScript that guarantees that the functional behavior of a program cannot be tampered with even if it is loaded by and executed within a malicious environment under the control of the attacker. As such, DJS is ideal for writing JavaScript security components, such as bookmarklets, single sign-on widgets, and cryptographic libraries, that may be ...

An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is char...

Dubin-Johnson syndrome (DJS) is a benign autosomal recessive liver disorder characterised by an intermittent jaundice caused by chronic and conjugated hyperbilirubinaemia. Many mutations in multidrug resistance associated protein (MRP-2) gene have been identified in patients with DJS. Although the disease is usually asymptomatic, some patients may experience vague abdominal pain. In this report...

This paper aims to show that the amenability of K1 ×K2 is equivalent to the following condition: “If φ is a continuous positive definite function defined on K1 ×K2 and φ ≥ 0 then the constant function 1K1×K2 belongs to the spectrum of φ”, which K1 and K2 are locally compact hypergroups as defined by R. Jewett [1], with convolutions ∗1, ∗2 respectively.Our study deals with the cases of exponenti...

Fortified Transposition Hypergroups appeared during the study of the theory of Formal Languages and Automata from the point of view of the hypercompositional structures theory. This paper studies the subhypergroups of these hypergroups and presents properties of their closed, symmetric, normal and reflexive subhypergroups.

We investigate amenability and weak amenability of the l1-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, for the hypergroup induced by Chebyshev polynomials of the first kind we prove amenability.

We study the concept of α-amenability of commutative hypergroups K. We establish several characterizations of α-amenability by combining results of [1] and [2] and adding the Glicksberg-Reiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed. 2000 Mathematics Subject Classification: Primary 43A62, Secondary 46H25

In this paper we study the Reiter P2 – condition for commutativ hypergroups and give necessary and sufficient conditions for x ∈ supp π, where π is the Plancherel measure. Finally we apply the general results to characterize supp π in the case of polynomial hypergroups. AMS Subject Classification (1991):43A62, 42C05, 43A07