We show that the non-superstability (non-stability) of a theory T is equivalent to the condition that for every elementary chain of length u; (un) of saturated models Mi of T with ||M,+i|| > ||M;|| for all s < UJ(U/I), the union of the chain is not saturated. The cardinality of T is immaterial.

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

In this article, we give a partial description of the sandpile group of the cone of the cartesian product of graphs in function of the sandpile group of the cone of their factors. Also, we introduce the concept of uniform homomorphism of graphs and prove that every surjective uniform homomorphism of graphs induces an injective homomorphism between their sandpile groups. As an application of the...

In this research article, a new connection between serial fuzzy relations and an extended version of rough sets in algebraic structure quantale is established. The notion consists successor class overlap the element quantale. Thus approximation space based on via overlaps quantales, are introduced. main purpose study to provide basic structures fuzzy-relations. way, acquires certain appealing p...

In the present paper, the Hyers-Ulam stability and also the superstability of double centralizers and multipliers on Banach algebras are established by using a fixed point method. With this method, the condition of without order on Banach algebras is no longer necessary.

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...

A recent result has demonstrated that the Bethe partition function always lower bounds the true partition function of binary, logsupermodular graphical models. We demonstrate that these results can be extended to other interesting classes of graphical models that are not necessarily binary or log-supermodular: the ferromagnetic Potts model with a uniform external field and its generalizations a...

ELEMENTARY CLASSES RAMI GROSSBERG AND SEBASTIEN VASEY Abstract. In the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the assumption that the class is tame and stable, we show that (asymptotically) no lon...

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

Let K be a field of characteristic 0, f : N → K be a multiplicative function, and F (z) = P n≥1 f (n)z n ∈ K[[z]] be algebraic over K(z). Then either there is a natural number k and a periodic multiplicative function χ(n) such that f (n) = n k χ(n) for all n, or f (n) is eventually zero. In particular , the generating function of a multiplicative function f : N → K is either transcendental or r...