Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on infinite words, captured by a deterministic two-way transducer, can be described with a regular transducer expression (RTE). For infinite words, the transducer us...

in this paper the class of n-ary hypergroups is introduced and several properties are found andexamples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of marty. on theother hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. we define thefundamental relation β* on an n-ary hypergroup h as the smallest equivalence relation such tha...

In this paper we introduce the smallest equivalence relation ξ∗ on a finite fuzzy hypergroup S such that the quotient group S/ξ∗, the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.

In this paper, we are going to introduce a fundamental relation on \(H_{v}BE\)-algebra and investigate some of properties, also construct new \((H_{v})BE\)-algebras via relation. We show that quotient any regular regulation is an quotient, strongly \(BE\)-algebra. Furthermore consider under what conditions relations transitive.

We examine photonic crystals PhC made of periodic stacks of anisotropic dielectric layers with a split band edge SBE on the band diagram. Just below the band edge frequency, the dispersion relation k of SBE PhCs can be approximated as a linear combination of a quadratic term and a quartic term. This is in contrast to regular conventional band edge PhCs, which produce a quadratic dispersion rela...

In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. Commutative fundamental rings and the fundamental relation α which is the smallest strongly regular relation in hyperringswere introduced by Davvaz and Vougiouklis (2007). Recently, another strongly regular relation named θ on hyperrings has been studied by Ameri and Norouzi (2013). Ameri...

This paper concerns pinched surfaces, also known as pseudosurfaces. A map is a graph G embedded on an oriented pinched surface. An arc of a map is an edge of G with a fixed direction. A regular map is one with a group of orientation-preserving automorphisms that acts regularly on the arcs of a map, i.e., that acts both freely and transitively. We study regular maps on pinched surfaces. We give ...