At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...

Abstract The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of normal First we define concept zero-divisors over hypermodule based it introduce class hypermodules, one divisible After presenting some their fundamental properties, will show that R -hypermodules M coincide whenever hyperring with no . Finally...

In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Furthermore, continuity properties and the relation to infinitely...

ABSTRAC"T A construction method for semiregular group divisible designs is given. This method can be applied to yield many classes of (in general, non-symmetric) semiregular group divisible designs whose duals are semiregular group divisible. In particular, the method can be used to construct many classes of transversal designs whose duals are serniregular group divisible designs, but not trans...

In this paper we analyze MapReduce distributed computations as divisible load scheduling problem. The two operations of mapping and reducing can be understood as two divisible applications with precedence constraints. A divisible load model is proposed, and schedule dominance properties are analyzed. We investigate dominant schedule structures for MapReduce computations. To our best knowledge t...