applications of hypergroups have mainly appeared in special subclasses. one of the important subclasses is the class of polygroups. in this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. in particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.

A voice is missing from the electronic dance music (EDM) industry: whether in prominent festival line-ups like Tomorrowland and Ultra Music Festival, or press that features achievements of top stars, women are underrepresented. Indeed, EDM industry has long been male-dominated permeated with gender imbalance. Only until last decade did gap begin to close: since 2012, investigations examining ra...

Explicit product formulas are obtained for families of multivariate polynomials which are orthogonal on simplices and on a parabolic biangle in R. These product formulas are shown to give rise to measure algebras which are hypergroups. The article also includes an elementary proof that the Michael topology for the space of compact subsets of a topological space (which is used in the definition ...

Let H be an ultraspherical hypergroup associated to a locally compact group G and let A(H) the Fourier algebra of H. For left Banach A(H)-submodule X VN(H), define QX norm closure linear span set {u f : u ?A(H), ? X} in BA(H)(A(H),X

Let K be a locally compact hypergroup. In this paper, among other results we give sufficient condition for the inclusion LΦ1w (K) * LΦ2w ⊆ to hold. Also, as an application, provide new weighted Orlicz space LΦw convolution Banach algebra.

This thesis focuses on the analysis and modeling of scratching, in other words, the DJ (disk jockey) practice of using the turntable as a musical instrument. There has been experimental use of turntables as musical instruments since their invention, but the use is now mainly ascribed to the musical genre hip-hop and the playing style known as scratching. Scratching has developed to become a ski...

Let {Rn} and {Pn} be two polynomial systems which induce signed polynomial hypergroup structures on N0. We investigate when the Banach algebra l(N0, h) can be continuously embedded into or is isomorphic to l(N0, h ). We find sufficient conditions on the connection coefficients cnk given by Rn = ∑n k=0 cnkPk, for the existence of such an embedding or isomorphism. Finally we apply these results t...