In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

Refinement plays a crucial role in “top-down” styles of verification, such as the refinement calculus, but for probabilistic systems proof of refinement is a particularly challenging task due to the combination of probability and nondeterminism which typically arises in partiallyspecified systems. Whilst the theory of probabilistic refinement is well-known [19] there are few tools to help with ...

This short paper arose as a warm-up to the more difficult computations at the primes 2 and 3 of connective versions of Behrens’ Q(2) spectrum, a spectrum conjecturally describing half of the K(2)-local sphere [2]. The natural starting case is to understand the K(1)-local story, giving rise to the present discussion of the homology of the connective image of J spectrum. The homology results are ...

A Fibonacci expansion of a nonnegative integer n is an expression of n as a sum of Fibonacci numbers Fk with k > 2. It may be thought of as a partition of n into Fibonacci parts. The most commonly studied such expansion is the unique one in which the parts are all distinct and no two consecutive Fibonacci numbers appear. C. G. Lekkerkerker first showed this expansion was unique in 1952 [5]. The...

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

In this paper we review the concepts of the superalgebra, superderivation and some properties of them. We will define algebraic and differential superderivations on a superalgebra and will prove some theorems about them, Then we consider a superalgebra bundle, that is an algebra bundle which its fibers are superalgebras and then characterize the superderivations of the algebra of sections of th...

Let A be a Banach algebra. A is called ideally amenable if for every closed ideal I of A, the first cohomology group of A with coefficients in I* is trivial. We investigate the closed ideals I for which H1 (A,I* )={0}, whenever A is weakly amenable or a biflat Banach algebra. Also we give some hereditary properties of ideal amenability.

recently, the algebraic theory of mv -algebras is intensively studied. in this paper, we extend the concept of derivation of $mv$-algebras and we give someillustrative examples. moreover, as a generalization of derivations of $mv$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $mv$-algebras.also, we investigate some properties of them.

In order for relation extraction systems to obtain human-level performance, they must be able to incorporate relational patterns inherent in the data (for example, that one’s sister is likely one’s mother’s daughter, or that children are likely to attend the same college as their parents). Hand-coding such knowledge can be time-consuming and inadequate. Additionally, there may exist many intere...