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 article we generalize the notion of complete parts, by introducing a weaker condition in definition. Using this generalization we define and analyse a new class of semihypergroups, which are called weak complete semihypergroups. Complete parts were introduced about 40 years ago by M. Koskas and they represent a basic notion of hyperstucture theory, utilized in constructing an important ...

in this paper, the notion of $psi -$weak contraction cite{rhoades} isextended to fuzzy metric spaces. the existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. our resultgeneralizes a result of gregori and sapena cite{gregori}.

Weak designs were defined in [10] and are used in constructions of extractors. Roughly speaking, a weak design is a collection of subsets satisfying some near-disjointness properties. Constructions of weak designs with certain parameters are given in [10]. These constructions are explicit in the sense that they require time and space polynomial in the number of subsets. However, the constructio...

We explore the nature of the classical propagation of light through media with strong frequency-dependent dispersion in the presence of a gravitational field. In the weak field limit, gravity causes a redshift of the optical frequency, which the slow-light medium converts into a spatially varying index of refraction. This results in the bending of a light ray in the medium. We further propose e...

In this paper we propose a notion of weak bisimulation for a class of weighted automata with unobservable transitions where weights are taken from an idempotent semiring. In particular the (max/+), (min/+) or (max/min) dioid are considered. The proposed bisimulation is a natural extension of Milner’s well known weak bisimulation for untimed automata (i. e., weighted automata over the boolean se...

The principle of weak monotonicity for cooperative games states that if a game changes so that the worth of the grand coalition and some player’s marginal contribution to all coalitions increase or stay the same, then this player’s payoff should not decrease. We investigate the class of values that satisfy effi ciency, symmetry, and weak monotonicity. It turns out that this class coincides with...