Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic structure on a semihypergroup pause a serious challenge in extending results from semigroups. We use the notion of concretization or pseudomultiplication, to prove some results on weak convergence of the sequence of averages of convolution powers of probability measures on topological semihypergroups...

This paper is the results of the ideas suggested by P. Corsini in his paper [10]. Our investigations take in account the paper [13] of I. Cristea. We study the hypergroup generated by the cosets modulo a subgroup (normal subgroup). We prove that (G/H, ◦4) is a complete hypergroup. We take many particular examples to illustrate some known results on hypergroups. Keyword: fuzzy sets, hypergroups,...

Using groups of affine transformations of linearly ordered fields a certain construction of non-commutative join hypergroups is presented based on the criterion of reproducibility of semi-hypergroups which are determined by ordered semigroups. The aim of this paper is to construct the abelization of the non-commutative join space of affine transformations of ordered fields. A construction of co...

Let (Rn(x))n∈N0 be an orthogonal sequence inducing a polynomial hypergroup on N0. The basic facts on polynomial hypergroups and their characters can be found in the monograph [1] or in the papers [6, 7]. A recent review is [8]. The Banach space of almost periodic functions on hypergroups is introduced and studied by the author in [5]. Weakly almost periodic functions are the topic of [12]. It i...

In this paper, we study hypergroups determined by lattices introduced by Varlet and Comer, especially we enumerate Varlet and Comer hypergroups of orders less than 50 and 13, respectively. 1 Basic definitions and results An algebraic hyperstructure is a natural generalization of a classical algebraic structure. More precisely, an algebraic hyperstructure is a non-empty set H endowed with one or...

Studies of musical training demonstrate functional advantages in rhythm tasks that result from enriched auditory experience. Anatomical correlates exist in brain areas involved in auditory perception, speech processing, motor control, attention, and emotion. However, these studies fail to include many classes of musicians that might undergo experience-related change. The current study examined ...

Musical perception is non-visual and people cannot describe what a song sounds like without listening to it. To facilitate music browsing and searching, we explore the automatic generation of visual thumbnails for music. Targeting an expert user groups, DJs, we developed a concept named ThumbnailDJ: Based on a metaphor of music notation, a visual thumbnail can be automatically generated for an ...

Exponential monomials are the basic building bricks of spectral analysis and spectral synthesis on Abelian groups. Recently there have been some attempts to extend the most important spectral analysis and spectral synthesis results from groups to hypergroups. For this purpose it is necessary to introduce a reasonable concept of exponential monomials. In this work we reconsider this problem, and...

The purpose of this paper is to compute of fundamental relations of hypergroups. In this regards first we study some basic properties of fundamental relation of hypergroups, then we show that any given group is isomorphic to the fundamental group of a nontrivial hypergroup. Finally we study the connections between categories of hypergroups and groups via the fundam...