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.

A series of cobalt complexes with pentadentate pyridine-rich ligands is studied. An initial Co(II) amine complex 1 is prone to aerial oxidation yielding a Co(III) imine complex 2 that is further converted into an amide complex 4 in presence of adventitious water. Introduction of an N-methyl protecting group to the ligand inhibits this oxidation and gives rise to the Co(II) species 5. Both the C...

Hot-electron transport in Co/Cu/Co trilayer films has been studied in the energy range from 1.0 to 2.0 eV using ballistic electron magnetic microscopy. Both the spin-dependent attenuation lengths of Co and the cumulative polarizing effects of spin-dependent tunneling and transmission across a Co/Cu interface have been determined. For very thin (a few A) Co layers, the latter effects result in a...

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 investigate effects of galaxy-galaxy interaction on the Tully-Fisher relation. The HI linewidth in interacting galaxies is significantly broader than the CO linewidth, and the HI to CO linewidth ratio is proportional to the strength of interaction. This provides different distances to galaxies measured by the Tully-Fisher relation with the CO and HI linewidths. Distances derived from the HI ...

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 $q$-...

We prove general adjoint functor theorems for weakly (co)complete $n$-categories. This class of $n$-categories includes the homotopy $\infty$-categories -- in particular, these do not admit all small (co)limits general. also introduce Brown representability (homotopy) and a theorem localizations compactly generated presentable if $n \geq 2$ stable any 1$.

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 ...

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...