in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

In this paper we study the module contractibility ofBanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. Also weinvestigate module contractibility of Banach algebras with theconcept of the module diagonal.

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

We generalize the notion of ‘diagonal’ from the class of CSL algebras to masa bimodules. We prove that a reflexive masa bimodule decomposes as a sum of two bimodules, the diagonal and a module generalizing the w*-closure of the Jacobson radical of a CSL algebra. The latter module turns out to be reflexive, a result which is new even for CSL algebras. We show that the projection onto the direct ...

We present an optimized design for GaAs/AlGaAs quantum cascade lasers operating at ‎‎4.1THz. This was based on a three-well active module with diagonal radiative transition. This ‎was performed by modifying the existing model structure, to reduce the parasitic anticrossings ‎‎(leakage currents) as well as the optical gain linewidth. While the gain FWHM was reduced by ‎more than 50% the gain pea...

This paper presents the rudiments of Hilbert-Mumford Intersection (HMI) theory: intersection theory on the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension. We introduce an additive group of geometric cycles, called ’tautological module’, generated by diagonal loci, node scrolls, and twists thereof. We determine recursively the intersection act...

We continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on Rn with integer entries, focusing on the construction of a projective multi-resolution analysis corresponding to dilations whose domains are finitely generated projective modules over continuous complex-valued functions on ntori, n ≥ 3. We are able to generalize some of these results to dila...

In this paper we construct a cylindrical module A♮H for an Hcomodule algebra A, where the antipode of the Hopf algebra H is bijective. We show that the cyclic module associated to the diagonal of A♮H is isomorphic with the cyclic module of the crossed product algebra A ⋊H. This enables us to derive a spectral sequence for the cyclic homology of the crossed product algebra. We also construct a c...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

We introduce the cylindrical module A♮H, where H is a Hopf algebra with S2 = idH and A is a Hopf module algebra over H. We show that there exists a cyclic map between the cyclic module of the crossed product algebra A⋊H and ∆(A♮H), the cyclic module related to the diagonal of A♮H. In the cocommutative case, ∆(A♮H) ∼= C•(A ⋊H). Finally we approximate ∆(A♮H) by a spectral sequence and we give an ...