let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.

It is proved that there is no structure of left (right) cancelative semigroup on [L]-dimensional universal space for the class of separable compact spaces of extensional dimension ≤ [L]. Besides, we note that the homeomorphism group of [L]-dimensional space whose nonempty open sets are universal for the class of separable compact spaces of extensional dimension ≤ [L] is totally disconnected.

Let (M,ω) be a compact symplectic 2n-manifold, and g a Riemannian metric on M compatible with ω. For instance, g could be Kähler, with Kähler form ω. Consider compact Lagrangian submanifolds L of M. We call L Hamiltonian stationary, or H-minimal, if it is a critical point of the volume functional Volg under Hamiltonian deformations, computing Volg (L) using g|L. It is called Hamiltonian stable ...

This paper studies algebraic frames L and the set Min(L) of minimal prime elements of L. We will endow the set Min(L) with two well-known topologies, known as the Hullkernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min(L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min(L) ...

We have shown that CdS and CdSe nanoparticles can act as very efficient and highly chemoselective photocatalysts for the reduction of aromatic azides to aromatic amines. In several cases, the reaction proceeds with quantum yields near 0.5, which approaches the theoretical maximum for a two-electron process. The wide scope of the reaction was confirmed with compounds containing electron withdraw...

In this paper, we study the evolution of L p-forms under Ricci flow with bounded curvature on a complete non-compact or a compact Riemannian manifold. We show that under curvature pinching conditions on such a manifold, the L norm of a smooth p-form is non-increasing along the Ricci flow. The L∞ norm is showed to have monotonicity property too.

Let G be a locally compact group. Then G is known to be amenable if and only if it satisfies property (P1), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα −mα‖ = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x ). We give a formulation of propety (P1) that extends naturally to locally compact quantum groups in ...

Crisp and L-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or L-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice. The categories of ambiguous and L-ambiguous representations are defined and investigated.