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.

We present a numerical study of essentially nonlinear dynamics surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation shear flow is known to have two branches; one which weakly dispersive for long waves. Weakly evolution the this branch can be described by Benjamin–Ono equation, integrable and has soliton multi-sol...

An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree T of a certain type on a space X is presumed to have a branch with some property. It is shown that then X can be embedded into a space with an FDD (Ei) so that all normalized sequences in X which are alm...

Abstract We study the total branch length Ln of the Bolthausen-Sznitman coalescent as the sample size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is shown that Ln/E(Ln) converges to 1 in probability and that Ln, properly normalized, converges weakly to a stable random variable as n tends to infinity. The results are applied to derive a corresponding limiti...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

We consider a class of dynamical systems, which we call weakly coarse expanding, is generalization to the postcritically infinite case expanding Thurston maps as discussed by Bonk-Meyer and closely related conformal systems defined Haissinsky-Pilgrim. prove existence uniqueness equilibrium states for wide potentials, well statistical laws such central limit theorem, law iterated logarithm, expo...

in this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. we prove that if $n$ is a weakly prime subtractive ternary subsemimodule of a ternary $r$-semimodule $m$, then either $n$ is a prime ternary subsemimodule or $(n : m)(n : m)n = 0$. if $n$ is a $q$-...

A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system insensitive to changes other. These can arise number contexts, and presence functions has interesting consequences for emergent dynamics. In this paper, we consider zones general coupled systems. For weakly limit cycle oscillators, investigate criteria that give rise functions. W...

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

The tropical arboreal environment is a mechanically complex and varied habitat. Arboreal inhabitants must adapt to changes in the compliance and stability of supports when moving around trees. Because the orangutan is the largest habitual arboreal inhabitant, it is unusually susceptible to branch compliance and stability and therefore represents a unique animal model to help investigate how ani...