Let A be an associative algebra with identity and with trace. We study the family of planar algebras on 1-boxes that arise from A in the work of Jones, but with the added assumption that the labels on the 1-boxes come from a discrete hypergroup in the sense of Sunder. This construction equips the algebra P A n with a canonical basis, B A n , which turns out to be a \tabular" basis. We examine s...

The measure algebras of the title are those which are also hypergroups with some regularity conditions, Examples include the convolutions associated with Jacobi polynomial series and Fourier Bessel series, It is shown here that there is a one-to-one correspondence between these hypergroups and a class of Sturm-Liouville problems which have the characters of the hypergroup as eigenfunctions, The...

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals

The paper investigates down-sets associated to well quasi orders. Of particular language-theoretic interest is the quasi order u s v (resp.u P v) of u being a subword (resp. a Parikh subword) of v, as well as their inverses. We establish a number of results about the regularity and e ective regularity of the down-sets, in particular, a general condition for the e ective regularity of the down-s...

in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...

A quasi-Dammann grating is proposed to generate array spots with proportional-intensity orders in the far field. To describe the performance of the grating, the uniformities of the array spots are redefined. A two-dimensional even-sampling encode scheme is adopted to design the quasi-Dammann grating. Numerical solutions of the binary-phase quasi-Dammann grating with proportional-intensity order...

Setting of this paper is Bishop's constructive mathematics. For a relation σ on a set with apartness is called quasi-antiorder if it is consistent and cotransitive. The quasi-antiorder σ is complete if holds . 0 1 / = σ σ − ∩ In this paper the following assertion ‘A quasi-antiorder is the intersection of a collection of quasi-antiorders.’ is given.

In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type BC. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds G/K over one of the (skew) fields F = R,C,H. We write the product formula of thes...

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 ...