In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

In this paper, we have developed several concepts such as the tree concept, short cycle concept and group shuffling of a propagation to decrypt low-density parity-check (LDPC) codes. Thus, proposed an algorithm based on where probability occurrence takes exponential form factor appearance belief propagation-group shuffled (EFAP-GSBP). This is used for wireless communication applications by prov...

In this article, we consider an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group Hn. We completely characterize exponents α,β γ such that is bounded from Lp(Hn,|x|αp)×Lq(Hn,|x|βq) to Lr(Hn,|x|−γr). Also, analogous sharp results are obtained Euclidean space.